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    <link:label id="lab_us-gaap_AdjustmentsToReconcileNetIncomeLossToCashProvidedByUsedInOperatingActivitiesAbstract_label_en-US" xlink:label="lab_us-gaap_AdjustmentsToReconcileNetIncomeLossToCashProvidedByUsedInOperatingActivitiesAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Adjustments to Reconcile Net Income (Loss) to Cash Provided by (Used in) Operating Activities [Abstract]</link:label>
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    <link:label id="lab_us-gaap_InterestExpenseOtherLongTermDebt_label_en-US" xlink:label="lab_us-gaap_InterestExpenseOtherLongTermDebt" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Interest Expense, Other Long-Term Debt</link:label>
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    <link:label id="lab_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueAfterYearFive_8f4f1490-a31a-41da-9ea3-a72c668b7f3b_terseLabel_en-US" xlink:label="lab_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueAfterYearFive" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Thereafter</link:label>
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    <link:label id="lab_us-gaap_BusinessAcquisitionPercentageOfVotingInterestsAcquired_eef38e0c-b4e4-4b48-a4d0-7042221a605f_verboseLabel_en-US" xlink:label="lab_us-gaap_BusinessAcquisitionPercentageOfVotingInterestsAcquired" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Share of the voting interest percentage</link:label>
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    <link:label id="lab_us-gaap_BusinessAcquisitionPercentageOfVotingInterestsAcquired_label_en-US" xlink:label="lab_us-gaap_BusinessAcquisitionPercentageOfVotingInterestsAcquired" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Business Acquisition, Percentage of Voting Interests Acquired</link:label>
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    <link:label id="lab_us-gaap_ComprehensiveIncomeNetOfTaxIncludingPortionAttributableToNoncontrollingInterest_5eede250-8eb3-46e4-b757-2d0195288057_totalLabel_en-US" xlink:label="lab_us-gaap_ComprehensiveIncomeNetOfTaxIncludingPortionAttributableToNoncontrollingInterest" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Total comprehensive income, net of tax</link:label>
    <link:label id="lab_us-gaap_ComprehensiveIncomeNetOfTaxIncludingPortionAttributableToNoncontrollingInterest_label_en-US" xlink:label="lab_us-gaap_ComprehensiveIncomeNetOfTaxIncludingPortionAttributableToNoncontrollingInterest" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Comprehensive Income (Loss), Net of Tax, Including Portion Attributable to Noncontrolling Interest</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ComprehensiveIncomeNetOfTaxIncludingPortionAttributableToNoncontrollingInterest" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_ComprehensiveIncomeNetOfTaxIncludingPortionAttributableToNoncontrollingInterest"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ComprehensiveIncomeNetOfTaxIncludingPortionAttributableToNoncontrollingInterest" xlink:to="lab_us-gaap_ComprehensiveIncomeNetOfTaxIncludingPortionAttributableToNoncontrollingInterest" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_NonNeosMember_terseLabel_en-US" xlink:label="lab_ecd_NonNeosMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Non-NEOs</link:label>
    <link:label id="lab_ecd_NonNeosMember_label_en-US" xlink:label="lab_ecd_NonNeosMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Non-NEOs [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_NonNeosMember" xlink:href="https://xbrl.sec.gov/ecd/2024/ecd-2024.xsd#ecd_NonNeosMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_NonNeosMember" xlink:to="lab_ecd_NonNeosMember" xlink:type="arc" order="1"/>
    <link:label id="lab_codi_AltorMember_449304bc-44be-4a24-b1b5-22a4747ade6b_terseLabel_en-US" xlink:label="lab_codi_AltorMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Altor</link:label>
    <link:label id="lab_codi_AltorMember_label_en-US" xlink:label="lab_codi_AltorMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Altor [Member]</link:label>
    <link:label id="lab_codi_AltorMember_documentation_en-US" xlink:label="lab_codi_AltorMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Altor</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_codi_AltorMember" xlink:href="codi-20241231.xsd#codi_AltorMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_codi_AltorMember" xlink:to="lab_codi_AltorMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CommonStockDividendsPerShareDeclared_8e8b4b4a-7d16-4154-acd9-ebc076347600_terseLabel_en-US" xlink:label="lab_us-gaap_CommonStockDividendsPerShareDeclared" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Cash distribution declared per share (refer to Note J)</link:label>
    <link:label id="lab_us-gaap_CommonStockDividendsPerShareDeclared_label_en-US" xlink:label="lab_us-gaap_CommonStockDividendsPerShareDeclared" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Common Stock, Dividends, Per Share, Declared</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CommonStockDividendsPerShareDeclared" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_CommonStockDividendsPerShareDeclared"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CommonStockDividendsPerShareDeclared" xlink:to="lab_us-gaap_CommonStockDividendsPerShareDeclared" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_GoodwillAndIntangibleAssetsGoodwillPolicy_b7d61329-19b1-4a27-b539-631d3853692f_terseLabel_en-US" xlink:label="lab_us-gaap_GoodwillAndIntangibleAssetsGoodwillPolicy" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Goodwill</link:label>
    <link:label id="lab_us-gaap_GoodwillAndIntangibleAssetsGoodwillPolicy_label_en-US" xlink:label="lab_us-gaap_GoodwillAndIntangibleAssetsGoodwillPolicy" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Goodwill and Intangible Assets, Goodwill, Policy [Policy Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_GoodwillAndIntangibleAssetsGoodwillPolicy" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_GoodwillAndIntangibleAssetsGoodwillPolicy"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_GoodwillAndIntangibleAssetsGoodwillPolicy" xlink:to="lab_us-gaap_GoodwillAndIntangibleAssetsGoodwillPolicy" xlink:type="arc" order="1"/>
    <link:label id="lab_codi_LeaseLiability_ea4f5c26-fea0-4b41-853d-380d777db9de_terseLabel_en-US" xlink:label="lab_codi_LeaseLiability" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Lease, Liability</link:label>
    <link:label id="lab_codi_LeaseLiability_label_en-US" xlink:label="lab_codi_LeaseLiability" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Lease, Liability</link:label>
    <link:label id="lab_codi_LeaseLiability_documentation_en-US" xlink:label="lab_codi_LeaseLiability" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Lease, Liability</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_codi_LeaseLiability" xlink:href="codi-20241231.xsd#codi_LeaseLiability"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_codi_LeaseLiability" xlink:to="lab_codi_LeaseLiability" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DefinedBenefitPlanExpectedFutureBenefitPaymentsYearThree_dd4de131-ee9e-49cf-9713-0110ec244d33_terseLabel_en-US" xlink:label="lab_us-gaap_DefinedBenefitPlanExpectedFutureBenefitPaymentsYearThree" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">2022</link:label>
    <link:label id="lab_us-gaap_DefinedBenefitPlanExpectedFutureBenefitPaymentsYearThree_label_en-US" xlink:label="lab_us-gaap_DefinedBenefitPlanExpectedFutureBenefitPaymentsYearThree" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Defined Benefit Plan, Expected Future Benefit Payment, Year Three</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DefinedBenefitPlanExpectedFutureBenefitPaymentsYearThree" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_DefinedBenefitPlanExpectedFutureBenefitPaymentsYearThree"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DefinedBenefitPlanExpectedFutureBenefitPaymentsYearThree" xlink:to="lab_us-gaap_DefinedBenefitPlanExpectedFutureBenefitPaymentsYearThree" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AllowanceForDoubtfulAccountsReceivableCurrent_dd855f95-57af-452d-a4c4-5f6aa6786a47_terseLabel_en-US" xlink:label="lab_us-gaap_AllowanceForDoubtfulAccountsReceivableCurrent" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Allowance for doubtful accounts receivable</link:label>
    <link:label id="lab_us-gaap_AllowanceForDoubtfulAccountsReceivableCurrent_45c0adf1-a168-4abf-baed-2ae2b6e1db63_negatedLabel_en-US" xlink:label="lab_us-gaap_AllowanceForDoubtfulAccountsReceivableCurrent" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:type="resource" xml:lang="en-US">Allowance for doubtful accounts</link:label>
    <link:label id="lab_us-gaap_AllowanceForDoubtfulAccountsReceivableCurrent_label_en-US" xlink:label="lab_us-gaap_AllowanceForDoubtfulAccountsReceivableCurrent" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Accounts Receivable, Allowance for Credit Loss, Current</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AllowanceForDoubtfulAccountsReceivableCurrent" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_AllowanceForDoubtfulAccountsReceivableCurrent"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AllowanceForDoubtfulAccountsReceivableCurrent" xlink:to="lab_us-gaap_AllowanceForDoubtfulAccountsReceivableCurrent" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_MinorityInterestDecreaseFromDistributionsToNoncontrollingInterestHolders_e7850b88-ed29-43cc-92b2-26c4684d3d19_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_MinorityInterestDecreaseFromDistributionsToNoncontrollingInterestHolders" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Noncontrolling Interest, Decrease from Distributions to Noncontrolling Interest Holders</link:label>
    <link:label id="lab_us-gaap_MinorityInterestDecreaseFromDistributionsToNoncontrollingInterestHolders_label_en-US" xlink:label="lab_us-gaap_MinorityInterestDecreaseFromDistributionsToNoncontrollingInterestHolders" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Noncontrolling Interest, Decrease from Distributions to Noncontrolling Interest Holders</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_MinorityInterestDecreaseFromDistributionsToNoncontrollingInterestHolders" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_MinorityInterestDecreaseFromDistributionsToNoncontrollingInterestHolders"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_MinorityInterestDecreaseFromDistributionsToNoncontrollingInterestHolders" xlink:to="lab_us-gaap_MinorityInterestDecreaseFromDistributionsToNoncontrollingInterestHolders" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DisposalGroupsIncludingDiscontinuedOperationsNameDomain_37f8c58c-cf99-473c-a0c5-3660a891ad02_terseLabel_en-US" xlink:label="lab_us-gaap_DisposalGroupsIncludingDiscontinuedOperationsNameDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Disposal Groups, Including Discontinued Operations, Name [Domain]</link:label>
    <link:label id="lab_us-gaap_DisposalGroupsIncludingDiscontinuedOperationsNameDomain_label_en-US" xlink:label="lab_us-gaap_DisposalGroupsIncludingDiscontinuedOperationsNameDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Disposal Group Name [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DisposalGroupsIncludingDiscontinuedOperationsNameDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_DisposalGroupsIncludingDiscontinuedOperationsNameDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DisposalGroupsIncludingDiscontinuedOperationsNameDomain" xlink:to="lab_us-gaap_DisposalGroupsIncludingDiscontinuedOperationsNameDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_IncomeTaxExaminationLineItems_1e68456e-f77c-4f08-a816-82cbe56deda7_terseLabel_en-US" xlink:label="lab_us-gaap_IncomeTaxExaminationLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Income Tax Examination [Line Items]</link:label>
    <link:label id="lab_us-gaap_IncomeTaxExaminationLineItems_label_en-US" xlink:label="lab_us-gaap_IncomeTaxExaminationLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Income Tax Examination [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncomeTaxExaminationLineItems" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_IncomeTaxExaminationLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_IncomeTaxExaminationLineItems" xlink:to="lab_us-gaap_IncomeTaxExaminationLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_IncreaseDecreaseInAccountsReceivable_fe90fb09-31a2-4a33-809e-bb02dfe9ea08_negatedLabel_en-US" xlink:label="lab_us-gaap_IncreaseDecreaseInAccountsReceivable" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:type="resource" xml:lang="en-US">Accounts receivable</link:label>
    <link:label id="lab_us-gaap_IncreaseDecreaseInAccountsReceivable_label_en-US" xlink:label="lab_us-gaap_IncreaseDecreaseInAccountsReceivable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Increase (Decrease) in Accounts Receivable</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncreaseDecreaseInAccountsReceivable" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_IncreaseDecreaseInAccountsReceivable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_IncreaseDecreaseInAccountsReceivable" xlink:to="lab_us-gaap_IncreaseDecreaseInAccountsReceivable" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_EarningsPerSharePolicyTextBlock_ca8a7354-4012-4ddd-a138-bd5a6175cfe8_terseLabel_en-US" xlink:label="lab_us-gaap_EarningsPerSharePolicyTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Earnings Per Common Share</link:label>
    <link:label id="lab_us-gaap_EarningsPerSharePolicyTextBlock_label_en-US" xlink:label="lab_us-gaap_EarningsPerSharePolicyTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Earnings Per Share, Policy [Policy Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_EarningsPerSharePolicyTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_EarningsPerSharePolicyTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_EarningsPerSharePolicyTextBlock" xlink:to="lab_us-gaap_EarningsPerSharePolicyTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_codi_A2022RevolvingCreditFacilityMember_37bba270-d14b-4243-b89f-cf86de0c5b1f_terseLabel_en-US" xlink:label="lab_codi_A2022RevolvingCreditFacilityMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">2022 Revolving Credit Facility</link:label>
    <link:label id="lab_codi_A2022RevolvingCreditFacilityMember_label_en-US" xlink:label="lab_codi_A2022RevolvingCreditFacilityMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">2022 Revolving Credit Facility [Member]</link:label>
    <link:label id="lab_codi_A2022RevolvingCreditFacilityMember_documentation_en-US" xlink:label="lab_codi_A2022RevolvingCreditFacilityMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">2022 Revolving Credit Facility</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_codi_A2022RevolvingCreditFacilityMember" xlink:href="codi-20241231.xsd#codi_A2022RevolvingCreditFacilityMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_codi_A2022RevolvingCreditFacilityMember" xlink:to="lab_codi_A2022RevolvingCreditFacilityMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_InventoryPolicyTextBlock_7c978f7e-ae8d-49c0-be43-28f84d764d4e_terseLabel_en-US" xlink:label="lab_us-gaap_InventoryPolicyTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Inventories</link:label>
    <link:label id="lab_us-gaap_InventoryPolicyTextBlock_label_en-US" xlink:label="lab_us-gaap_InventoryPolicyTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Inventory, Policy [Policy Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_InventoryPolicyTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_InventoryPolicyTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_InventoryPolicyTextBlock" xlink:to="lab_us-gaap_InventoryPolicyTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_NonRule10b51ArrAdoptedFlag_terseLabel_en-US" xlink:label="lab_ecd_NonRule10b51ArrAdoptedFlag" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Non-Rule 10b5-1 Arrangement Adopted</link:label>
    <link:label id="lab_ecd_NonRule10b51ArrAdoptedFlag_label_en-US" xlink:label="lab_ecd_NonRule10b51ArrAdoptedFlag" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Non-Rule 10b5-1 Arrangement Adopted [Flag]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_NonRule10b51ArrAdoptedFlag" xlink:href="https://xbrl.sec.gov/ecd/2024/ecd-2024.xsd#ecd_NonRule10b51ArrAdoptedFlag"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_NonRule10b51ArrAdoptedFlag" xlink:to="lab_ecd_NonRule10b51ArrAdoptedFlag" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_IncomeLossFromContinuingOperationsIncludingPortionAttributableToNoncontrollingInterest_c5718289-004d-42c2-a56a-79147dcbbc23_totalLabel_en-US" xlink:label="lab_us-gaap_IncomeLossFromContinuingOperationsIncludingPortionAttributableToNoncontrollingInterest" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Income (loss) from continuing operations</link:label>
    <link:label id="lab_us-gaap_IncomeLossFromContinuingOperationsIncludingPortionAttributableToNoncontrollingInterest_b31c8681-5449-48d8-817a-94473346ec1d_terseLabel_en-US" xlink:label="lab_us-gaap_IncomeLossFromContinuingOperationsIncludingPortionAttributableToNoncontrollingInterest" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Income (loss) from continuing operations</link:label>
    <link:label id="lab_us-gaap_IncomeLossFromContinuingOperationsIncludingPortionAttributableToNoncontrollingInterest_label_en-US" xlink:label="lab_us-gaap_IncomeLossFromContinuingOperationsIncludingPortionAttributableToNoncontrollingInterest" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Income (Loss) from Continuing Operations, Net of Tax, Including Portion Attributable to Noncontrolling Interest</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncomeLossFromContinuingOperationsIncludingPortionAttributableToNoncontrollingInterest" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_IncomeLossFromContinuingOperationsIncludingPortionAttributableToNoncontrollingInterest"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_IncomeLossFromContinuingOperationsIncludingPortionAttributableToNoncontrollingInterest" xlink:to="lab_us-gaap_IncomeLossFromContinuingOperationsIncludingPortionAttributableToNoncontrollingInterest" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FairValueDisclosuresTextBlock_ee6f7a61-deee-43bc-b74e-00c455e1eae3_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueDisclosuresTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Fair Value Measurement</link:label>
    <link:label id="lab_us-gaap_FairValueDisclosuresTextBlock_label_en-US" xlink:label="lab_us-gaap_FairValueDisclosuresTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fair Value Disclosures [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueDisclosuresTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_FairValueDisclosuresTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FairValueDisclosuresTextBlock" xlink:to="lab_us-gaap_FairValueDisclosuresTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_codi_Optionactivityattributabletononcontrollinginterestdiscontinuedops_7b0cdec6-d4d6-4de5-9354-28f631876752_terseLabel_en-US" xlink:label="lab_codi_Optionactivityattributabletononcontrollinginterestdiscontinuedops" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Option activity attributable to noncontrolling interest, discontinued ops</link:label>
    <link:label id="lab_codi_Optionactivityattributabletononcontrollinginterestdiscontinuedops_label_en-US" xlink:label="lab_codi_Optionactivityattributabletononcontrollinginterestdiscontinuedops" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Option activity attributable to noncontrolling interest, discontinued ops</link:label>
    <link:label id="lab_codi_Optionactivityattributabletononcontrollinginterestdiscontinuedops_documentation_en-US" xlink:label="lab_codi_Optionactivityattributabletononcontrollinginterestdiscontinuedops" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Option activity attributable to noncontrolling interest, discontinued ops</link:label>
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    <link:label id="lab_us-gaap_OtherComprehensiveIncomeLossBeforeTax_b11f3183-5bcc-40d6-8453-8566a3629932_terseLabel_en-US" xlink:label="lab_us-gaap_OtherComprehensiveIncomeLossBeforeTax" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Other Comprehensive Income (Loss), before Tax</link:label>
    <link:label id="lab_us-gaap_OtherComprehensiveIncomeLossBeforeTax_label_en-US" xlink:label="lab_us-gaap_OtherComprehensiveIncomeLossBeforeTax" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Other Comprehensive Income (Loss), before Tax</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OtherComprehensiveIncomeLossBeforeTax" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_OtherComprehensiveIncomeLossBeforeTax"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OtherComprehensiveIncomeLossBeforeTax" xlink:to="lab_us-gaap_OtherComprehensiveIncomeLossBeforeTax" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_AwardTmgDiscLineItems_label_en-US" xlink:label="lab_ecd_AwardTmgDiscLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Award Timing Disclosures [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_AwardTmgDiscLineItems" xlink:href="https://xbrl.sec.gov/ecd/2024/ecd-2024.xsd#ecd_AwardTmgDiscLineItems"/>
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    <link:label id="lab_us-gaap_EffectiveIncomeTaxRateReconciliationDispositionOfAssets_a850cf85-8192-4141-8f98-6d617d77fe96_terseLabel_en-US" xlink:label="lab_us-gaap_EffectiveIncomeTaxRateReconciliationDispositionOfAssets" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Effect of classification of assets held for sale</link:label>
    <link:label id="lab_us-gaap_EffectiveIncomeTaxRateReconciliationDispositionOfAssets_label_en-US" xlink:label="lab_us-gaap_EffectiveIncomeTaxRateReconciliationDispositionOfAssets" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Effective Income Tax Rate Reconciliation, Disposition of Asset, Percent</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_EffectiveIncomeTaxRateReconciliationDispositionOfAssets" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_EffectiveIncomeTaxRateReconciliationDispositionOfAssets"/>
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    <link:label id="lab_srt_EquityMethodInvesteeNameDomain_4dc714f9-66f8-4cb2-85cc-09e62bf7a4d2_terseLabel_en-US" xlink:label="lab_srt_EquityMethodInvesteeNameDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Investment, Name [Domain]</link:label>
    <link:label id="lab_srt_EquityMethodInvesteeNameDomain_label_en-US" xlink:label="lab_srt_EquityMethodInvesteeNameDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Investment, Name [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_srt_EquityMethodInvesteeNameDomain" xlink:href="https://xbrl.fasb.org/srt/2024/elts/srt-2024.xsd#srt_EquityMethodInvesteeNameDomain"/>
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    <link:label id="lab_us-gaap_RetirementPlanTaxStatusAxis_f9e818e6-3b8e-47a7-9db0-3e07247f5f97_terseLabel_en-US" xlink:label="lab_us-gaap_RetirementPlanTaxStatusAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Retirement Plan Tax Status [Axis]</link:label>
    <link:label id="lab_us-gaap_RetirementPlanTaxStatusAxis_label_en-US" xlink:label="lab_us-gaap_RetirementPlanTaxStatusAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Retirement Plan Tax Status [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_RetirementPlanTaxStatusAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_RetirementPlanTaxStatusAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_RetirementPlanTaxStatusAxis" xlink:to="lab_us-gaap_RetirementPlanTaxStatusAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_PortionAtFairValueFairValueDisclosureMember_3d709f1a-ff3e-4e0b-88b9-655468654987_terseLabel_en-US" xlink:label="lab_us-gaap_PortionAtFairValueFairValueDisclosureMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Portion at Fair Value Measurement [Member]</link:label>
    <link:label id="lab_us-gaap_PortionAtFairValueFairValueDisclosureMember_label_en-US" xlink:label="lab_us-gaap_PortionAtFairValueFairValueDisclosureMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Portion at Fair Value Measurement [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PortionAtFairValueFairValueDisclosureMember" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_PortionAtFairValueFairValueDisclosureMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PortionAtFairValueFairValueDisclosureMember" xlink:to="lab_us-gaap_PortionAtFairValueFairValueDisclosureMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OperatingLeaseLiabilityNoncurrentStatementOfFinancialPositionExtensibleList_1857f9b0-f83f-4ea9-9139-323507e4cc4f_terseLabel_en-US" xlink:label="lab_us-gaap_OperatingLeaseLiabilityNoncurrentStatementOfFinancialPositionExtensibleList" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Operating Lease, Liability, Noncurrent, Statement of Financial Position [Extensible List]</link:label>
    <link:label id="lab_us-gaap_OperatingLeaseLiabilityNoncurrentStatementOfFinancialPositionExtensibleList_label_en-US" xlink:label="lab_us-gaap_OperatingLeaseLiabilityNoncurrentStatementOfFinancialPositionExtensibleList" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Operating Lease, Liability, Noncurrent, Statement of Financial Position [Extensible Enumeration]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OperatingLeaseLiabilityNoncurrentStatementOfFinancialPositionExtensibleList" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_OperatingLeaseLiabilityNoncurrentStatementOfFinancialPositionExtensibleList"/>
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    <link:label id="lab_us-gaap_OffsettingAbstract_0d4c3a81-d4d9-4d60-8563-af00de5219cf_terseLabel_en-US" xlink:label="lab_us-gaap_OffsettingAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Offsetting [Abstract]</link:label>
    <link:label id="lab_us-gaap_OffsettingAbstract_label_en-US" xlink:label="lab_us-gaap_OffsettingAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Offsetting [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OffsettingAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_OffsettingAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OffsettingAbstract" xlink:to="lab_us-gaap_OffsettingAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DeferredTaxAssetsTaxCreditCarryforwards_587ee30b-3272-45fc-8a65-e3e805e78d78_terseLabel_en-US" xlink:label="lab_us-gaap_DeferredTaxAssetsTaxCreditCarryforwards" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Tax credits</link:label>
    <link:label id="lab_us-gaap_DeferredTaxAssetsTaxCreditCarryforwards_label_en-US" xlink:label="lab_us-gaap_DeferredTaxAssetsTaxCreditCarryforwards" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Deferred Tax Assets, Tax Credit Carryforwards</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DeferredTaxAssetsTaxCreditCarryforwards" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_DeferredTaxAssetsTaxCreditCarryforwards"/>
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    <link:label id="lab_us-gaap_GeographicDistributionAxis_7b509103-5e75-4ebd-9c86-97d637000a9e_terseLabel_en-US" xlink:label="lab_us-gaap_GeographicDistributionAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Geographic Distribution [Axis]</link:label>
    <link:label id="lab_us-gaap_GeographicDistributionAxis_label_en-US" xlink:label="lab_us-gaap_GeographicDistributionAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Geographic Distribution [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_GeographicDistributionAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_GeographicDistributionAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_GeographicDistributionAxis" xlink:to="lab_us-gaap_GeographicDistributionAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_RevenueFromContractWithCustomerAbstract_dc151b5d-533b-44a5-b9fc-605f1bd0733d_terseLabel_en-US" xlink:label="lab_us-gaap_RevenueFromContractWithCustomerAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Revenue from Contract with Customer [Abstract]</link:label>
    <link:label id="lab_us-gaap_RevenueFromContractWithCustomerAbstract_label_en-US" xlink:label="lab_us-gaap_RevenueFromContractWithCustomerAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Revenue from Contract with Customer [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_RevenueFromContractWithCustomerAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_RevenueFromContractWithCustomerAbstract"/>
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    <link:label id="lab_us-gaap_ValuationAllowancesAndReservesTypeAxis_ee1ef053-8e92-43af-9577-03373b1f906f_terseLabel_en-US" xlink:label="lab_us-gaap_ValuationAllowancesAndReservesTypeAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">SEC Schedule, 12-09, Valuation Allowances and Reserves Type [Axis]</link:label>
    <link:label id="lab_us-gaap_ValuationAllowancesAndReservesTypeAxis_label_en-US" xlink:label="lab_us-gaap_ValuationAllowancesAndReservesTypeAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">SEC Schedule, 12-09, Valuation Allowances and Reserves Type [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ValuationAllowancesAndReservesTypeAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_ValuationAllowancesAndReservesTypeAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ValuationAllowancesAndReservesTypeAxis" xlink:to="lab_us-gaap_ValuationAllowancesAndReservesTypeAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_country_US_8a19dc43-8d41-4feb-88e2-15f071378e83_terseLabel_en-US" xlink:label="lab_country_US" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">UNITED STATES</link:label>
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    <link:label id="lab_us-gaap_DisposalGroupIncludingDiscontinuedOperationCashAndCashEquivalents_77a2edb8-cd11-459e-84fe-edb53244dc83_terseLabel_en-US" xlink:label="lab_us-gaap_DisposalGroupIncludingDiscontinuedOperationCashAndCashEquivalents" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Cash</link:label>
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    <link:label id="lab_us-gaap_FiniteLivedIntangibleAssetsGross_d44af041-7a0d-49de-a868-2e46759249b5_terseLabel_en-US" xlink:label="lab_us-gaap_FiniteLivedIntangibleAssetsGross" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Finite-Lived Intangible Assets, Gross</link:label>
    <link:label id="lab_us-gaap_FiniteLivedIntangibleAssetsGross_label_en-US" xlink:label="lab_us-gaap_FiniteLivedIntangibleAssetsGross" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Finite-Lived Intangible Assets, Gross</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FiniteLivedIntangibleAssetsGross" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_FiniteLivedIntangibleAssetsGross"/>
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    <link:label id="lab_codi_LesseeOperatingAndFinancingLeaseLiabilityToBePaidYearTwo_aa1f7325-0108-4205-a2f3-4f117bda64a0_terseLabel_en-US" xlink:label="lab_codi_LesseeOperatingAndFinancingLeaseLiabilityToBePaidYearTwo" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Lessee Operating and Financing Lease, Liability, to be Paid, Year Two</link:label>
    <link:label id="lab_codi_LesseeOperatingAndFinancingLeaseLiabilityToBePaidYearTwo_label_en-US" xlink:label="lab_codi_LesseeOperatingAndFinancingLeaseLiabilityToBePaidYearTwo" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Lessee Operating and Financing Lease, Liability, to be Paid, Year Two</link:label>
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    <link:label id="lab_us-gaap_OperatingSegmentsMember_6e3d4db6-de09-40fd-b00c-878bcd91ab0c_terseLabel_en-US" xlink:label="lab_us-gaap_OperatingSegmentsMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Operating Segments</link:label>
    <link:label id="lab_us-gaap_OperatingSegmentsMember_label_en-US" xlink:label="lab_us-gaap_OperatingSegmentsMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Operating Segments [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OperatingSegmentsMember" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_OperatingSegmentsMember"/>
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    <link:label id="lab_us-gaap_NetCashProvidedByUsedInOperatingActivities_1ff37f50-ae25-44b0-aee1-2698bbeed929_totalLabel_en-US" xlink:label="lab_us-gaap_NetCashProvidedByUsedInOperatingActivities" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Net cash provided by (used in) operating activities</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_NetCashProvidedByUsedInOperatingActivities" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_NetCashProvidedByUsedInOperatingActivities"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_NetCashProvidedByUsedInOperatingActivities" xlink:to="lab_us-gaap_NetCashProvidedByUsedInOperatingActivities" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_NetCashProvidedByUsedInOperatingActivitiesAbstract_03a4a258-155b-4bf2-9ce2-f9e7e2f35c76_terseLabel_en-US" xlink:label="lab_us-gaap_NetCashProvidedByUsedInOperatingActivitiesAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Cash flows from operating activities:</link:label>
    <link:label id="lab_us-gaap_NetCashProvidedByUsedInOperatingActivitiesAbstract_label_en-US" xlink:label="lab_us-gaap_NetCashProvidedByUsedInOperatingActivitiesAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Net Cash Provided by (Used in) Operating Activities [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_NetCashProvidedByUsedInOperatingActivitiesAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_NetCashProvidedByUsedInOperatingActivitiesAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_NetCashProvidedByUsedInOperatingActivitiesAbstract" xlink:to="lab_us-gaap_NetCashProvidedByUsedInOperatingActivitiesAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_codi_AccruedProductRebates_7b72dc8b-225f-46cb-9dc8-0b7e388df486_terseLabel_en-US" xlink:label="lab_codi_AccruedProductRebates" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Accrued rebates and discounts</link:label>
    <link:label id="lab_codi_AccruedProductRebates_label_en-US" xlink:label="lab_codi_AccruedProductRebates" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Accrued Product Rebates</link:label>
    <link:label id="lab_codi_AccruedProductRebates_documentation_en-US" xlink:label="lab_codi_AccruedProductRebates" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Accrued Product Rebates</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_codi_AccruedProductRebates" xlink:href="codi-20241231.xsd#codi_AccruedProductRebates"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_codi_AccruedProductRebates" xlink:to="lab_codi_AccruedProductRebates" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OtherOwnershipInterestsByNameAxis_ddbefeee-18aa-4cf6-99c6-acd8bb24d4eb_terseLabel_en-US" xlink:label="lab_us-gaap_OtherOwnershipInterestsByNameAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Other Ownership Interests Name [Axis]</link:label>
    <link:label id="lab_us-gaap_OtherOwnershipInterestsByNameAxis_label_en-US" xlink:label="lab_us-gaap_OtherOwnershipInterestsByNameAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Other Ownership Interests Name [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OtherOwnershipInterestsByNameAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_OtherOwnershipInterestsByNameAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OtherOwnershipInterestsByNameAxis" xlink:to="lab_us-gaap_OtherOwnershipInterestsByNameAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_AwardTmgMethodTextBlock_terseLabel_en-US" xlink:label="lab_ecd_AwardTmgMethodTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Award Timing Method</link:label>
    <link:label id="lab_ecd_AwardTmgMethodTextBlock_label_en-US" xlink:label="lab_ecd_AwardTmgMethodTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Award Timing Method [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_AwardTmgMethodTextBlock" xlink:href="https://xbrl.sec.gov/ecd/2024/ecd-2024.xsd#ecd_AwardTmgMethodTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_AwardTmgMethodTextBlock" xlink:to="lab_ecd_AwardTmgMethodTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DefinedBenefitPlanNetPeriodicBenefitCost_0fe951aa-175a-478c-bb59-0859eb018a13_totalLabel_en-US" xlink:label="lab_us-gaap_DefinedBenefitPlanNetPeriodicBenefitCost" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Net periodic benefit cost</link:label>
    <link:label id="lab_us-gaap_DefinedBenefitPlanNetPeriodicBenefitCost_1dd64c40-518e-4184-89c8-0f9df9219674_terseLabel_en-US" xlink:label="lab_us-gaap_DefinedBenefitPlanNetPeriodicBenefitCost" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Defined Benefit Plan, Net Periodic Benefit Cost (Credit)</link:label>
    <link:label id="lab_us-gaap_DefinedBenefitPlanNetPeriodicBenefitCost_label_en-US" xlink:label="lab_us-gaap_DefinedBenefitPlanNetPeriodicBenefitCost" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Defined Benefit Plan, Net Periodic Benefit Cost (Credit)</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DefinedBenefitPlanNetPeriodicBenefitCost" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_DefinedBenefitPlanNetPeriodicBenefitCost"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DefinedBenefitPlanNetPeriodicBenefitCost" xlink:to="lab_us-gaap_DefinedBenefitPlanNetPeriodicBenefitCost" xlink:type="arc" order="1"/>
    <link:label id="lab_codi_QuarterlyIncentiveManagementFeePercentageOfEntityAdjustedNetAssets_17275c72-468c-4d33-8667-60808fe674e0_terseLabel_en-US" xlink:label="lab_codi_QuarterlyIncentiveManagementFeePercentageOfEntityAdjustedNetAssets" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Quarterly Incentive Management Fee Percentage Of Entity Adjusted Net Assets</link:label>
    <link:label id="lab_codi_QuarterlyIncentiveManagementFeePercentageOfEntityAdjustedNetAssets_label_en-US" xlink:label="lab_codi_QuarterlyIncentiveManagementFeePercentageOfEntityAdjustedNetAssets" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Quarterly Incentive Management Fee Percentage Of Entity Adjusted Net Assets</link:label>
    <link:label id="lab_codi_QuarterlyIncentiveManagementFeePercentageOfEntityAdjustedNetAssets_documentation_en-US" xlink:label="lab_codi_QuarterlyIncentiveManagementFeePercentageOfEntityAdjustedNetAssets" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Quarterly Incentive Management Fee Percentage Of Entity Adjusted Net Assets</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_codi_QuarterlyIncentiveManagementFeePercentageOfEntityAdjustedNetAssets" xlink:href="codi-20241231.xsd#codi_QuarterlyIncentiveManagementFeePercentageOfEntityAdjustedNetAssets"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_codi_QuarterlyIncentiveManagementFeePercentageOfEntityAdjustedNetAssets" xlink:to="lab_codi_QuarterlyIncentiveManagementFeePercentageOfEntityAdjustedNetAssets" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_TradingArrByIndTable_terseLabel_en-US" xlink:label="lab_ecd_TradingArrByIndTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Trading Arrangements, by Individual</link:label>
    <link:label id="lab_ecd_TradingArrByIndTable_label_en-US" xlink:label="lab_ecd_TradingArrByIndTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Trading Arrangements, by Individual [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_TradingArrByIndTable" xlink:href="https://xbrl.sec.gov/ecd/2024/ecd-2024.xsd#ecd_TradingArrByIndTable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_TradingArrByIndTable" xlink:to="lab_ecd_TradingArrByIndTable" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AcquiredFiniteLivedIntangibleAssetsLineItems_607bbf32-c4d0-4139-b09a-210425b0622b_terseLabel_en-US" xlink:label="lab_us-gaap_AcquiredFiniteLivedIntangibleAssetsLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Acquired Finite-Lived Intangible Assets [Line Items]</link:label>
    <link:label id="lab_us-gaap_AcquiredFiniteLivedIntangibleAssetsLineItems_label_en-US" xlink:label="lab_us-gaap_AcquiredFiniteLivedIntangibleAssetsLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Acquired Finite-Lived Intangible Assets [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AcquiredFiniteLivedIntangibleAssetsLineItems" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_AcquiredFiniteLivedIntangibleAssetsLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AcquiredFiniteLivedIntangibleAssetsLineItems" xlink:to="lab_us-gaap_AcquiredFiniteLivedIntangibleAssetsLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_MinorityInterestLineItems_76305307-223b-42c2-a843-0b426d816303_terseLabel_en-US" xlink:label="lab_us-gaap_MinorityInterestLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Noncontrolling Interest [Line Items]</link:label>
    <link:label id="lab_us-gaap_MinorityInterestLineItems_label_en-US" xlink:label="lab_us-gaap_MinorityInterestLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Noncontrolling Interest [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_MinorityInterestLineItems" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_MinorityInterestLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_MinorityInterestLineItems" xlink:to="lab_us-gaap_MinorityInterestLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FairValueByMeasurementFrequencyAxis_1f7d31fa-d482-49c4-9c74-43af1cd35404_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueByMeasurementFrequencyAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Measurement Frequency [Axis]</link:label>
    <link:label id="lab_us-gaap_FairValueByMeasurementFrequencyAxis_label_en-US" xlink:label="lab_us-gaap_FairValueByMeasurementFrequencyAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Measurement Frequency [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueByMeasurementFrequencyAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_FairValueByMeasurementFrequencyAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FairValueByMeasurementFrequencyAxis" xlink:to="lab_us-gaap_FairValueByMeasurementFrequencyAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_EntityCommonStockSharesOutstanding_5dd5ef6b-0ccd-4bc6-b85f-52acb43f2dde_terseLabel_en-US" xlink:label="lab_dei_EntityCommonStockSharesOutstanding" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Entity Common Stock, Shares Outstanding</link:label>
    <link:label id="lab_dei_EntityCommonStockSharesOutstanding_label_en-US" xlink:label="lab_dei_EntityCommonStockSharesOutstanding" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Entity Common Stock, Shares Outstanding</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityCommonStockSharesOutstanding" xlink:href="https://xbrl.sec.gov/dei/2024/dei-2024.xsd#dei_EntityCommonStockSharesOutstanding"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_EntityCommonStockSharesOutstanding" xlink:to="lab_dei_EntityCommonStockSharesOutstanding" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FinanceLeaseWeightedAverageRemainingLeaseTerm1_3020b2d1-28e3-45ce-9b0a-8e29118d5d67_terseLabel_en-US" xlink:label="lab_us-gaap_FinanceLeaseWeightedAverageRemainingLeaseTerm1" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Finance Lease, Weighted Average Remaining Lease Term</link:label>
    <link:label id="lab_us-gaap_FinanceLeaseWeightedAverageRemainingLeaseTerm1_label_en-US" xlink:label="lab_us-gaap_FinanceLeaseWeightedAverageRemainingLeaseTerm1" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Finance Lease, Weighted Average Remaining Lease Term</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FinanceLeaseWeightedAverageRemainingLeaseTerm1" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_FinanceLeaseWeightedAverageRemainingLeaseTerm1"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FinanceLeaseWeightedAverageRemainingLeaseTerm1" xlink:to="lab_us-gaap_FinanceLeaseWeightedAverageRemainingLeaseTerm1" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_InsiderTradingPoliciesProcLineItems_label_en-US" xlink:label="lab_ecd_InsiderTradingPoliciesProcLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Insider Trading Policies and Procedures [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_InsiderTradingPoliciesProcLineItems" xlink:href="https://xbrl.sec.gov/ecd/2024/ecd-2024.xsd#ecd_InsiderTradingPoliciesProcLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_InsiderTradingPoliciesProcLineItems" xlink:to="lab_ecd_InsiderTradingPoliciesProcLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_UseOfEstimates_27f000da-a4ab-4662-b25d-2d52b1c49a3b_terseLabel_en-US" xlink:label="lab_us-gaap_UseOfEstimates" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Use of Estimates</link:label>
    <link:label id="lab_us-gaap_UseOfEstimates_label_en-US" xlink:label="lab_us-gaap_UseOfEstimates" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Use of Estimates, Policy [Policy Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_UseOfEstimates" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_UseOfEstimates"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_UseOfEstimates" xlink:to="lab_us-gaap_UseOfEstimates" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_AdjToCompAmt_terseLabel_en-US" xlink:label="lab_ecd_AdjToCompAmt" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Adjustment to Compensation, Amount</link:label>
    <link:label id="lab_ecd_AdjToCompAmt_label_en-US" xlink:label="lab_ecd_AdjToCompAmt" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Adjustment to Compensation Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_AdjToCompAmt" xlink:href="https://xbrl.sec.gov/ecd/2024/ecd-2024.xsd#ecd_AdjToCompAmt"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_AdjToCompAmt" xlink:to="lab_ecd_AdjToCompAmt" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_PayablesAndAccrualsAbstract_6cfc0e53-89e2-41d1-a65d-c9c1a691a3e4_terseLabel_en-US" xlink:label="lab_us-gaap_PayablesAndAccrualsAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Payables and Accruals [Abstract]</link:label>
    <link:label id="lab_us-gaap_PayablesAndAccrualsAbstract_label_en-US" xlink:label="lab_us-gaap_PayablesAndAccrualsAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Payables and Accruals [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PayablesAndAccrualsAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_PayablesAndAccrualsAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PayablesAndAccrualsAbstract" xlink:to="lab_us-gaap_PayablesAndAccrualsAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_codi_IdentifiableAssetsOfSegments_e4fd918f-aeb2-4a34-bdeb-eeb8531fdf5b_terseLabel_en-US" xlink:label="lab_codi_IdentifiableAssetsOfSegments" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Identifiable assets of segments</link:label>
    <link:label id="lab_codi_IdentifiableAssetsOfSegments_label_en-US" xlink:label="lab_codi_IdentifiableAssetsOfSegments" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Identifiable Assets Of Segments</link:label>
    <link:label id="lab_codi_IdentifiableAssetsOfSegments_documentation_en-US" xlink:label="lab_codi_IdentifiableAssetsOfSegments" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Identifiable assets of segments exclude goodwill and accounts receivable balances previously disclosed.</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_codi_IdentifiableAssetsOfSegments" xlink:href="codi-20241231.xsd#codi_IdentifiableAssetsOfSegments"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_codi_IdentifiableAssetsOfSegments" xlink:to="lab_codi_IdentifiableAssetsOfSegments" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_OutstandingRecoveryCompAmt_terseLabel_en-US" xlink:label="lab_ecd_OutstandingRecoveryCompAmt" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Compensation Amount</link:label>
    <link:label id="lab_ecd_OutstandingRecoveryCompAmt_label_en-US" xlink:label="lab_ecd_OutstandingRecoveryCompAmt" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Outstanding Recovery Compensation Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_OutstandingRecoveryCompAmt" xlink:href="https://xbrl.sec.gov/ecd/2024/ecd-2024.xsd#ecd_OutstandingRecoveryCompAmt"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_OutstandingRecoveryCompAmt" xlink:to="lab_ecd_OutstandingRecoveryCompAmt" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DisposalGroupClassificationAxis_e918efcf-413f-4e18-8dd4-a76a69d8c75e_terseLabel_en-US" xlink:label="lab_us-gaap_DisposalGroupClassificationAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Disposal Group Classification [Axis]</link:label>
    <link:label id="lab_us-gaap_DisposalGroupClassificationAxis_label_en-US" xlink:label="lab_us-gaap_DisposalGroupClassificationAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Disposal Group Classification [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DisposalGroupClassificationAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_DisposalGroupClassificationAxis"/>
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    <link:label id="lab_us-gaap_BusinessAcquisitionProFormaInformationAbstract_6c3f4b24-385e-4580-bbf3-5ad14be79c54_terseLabel_en-US" xlink:label="lab_us-gaap_BusinessAcquisitionProFormaInformationAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Business Acquisition, Pro Forma Information [Abstract]</link:label>
    <link:label id="lab_us-gaap_BusinessAcquisitionProFormaInformationAbstract_label_en-US" xlink:label="lab_us-gaap_BusinessAcquisitionProFormaInformationAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Business Acquisition, Pro Forma Information [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_BusinessAcquisitionProFormaInformationAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_BusinessAcquisitionProFormaInformationAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_BusinessAcquisitionProFormaInformationAbstract" xlink:to="lab_us-gaap_BusinessAcquisitionProFormaInformationAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DisposalGroupIncludingDiscontinuedOperationAssetsNoncurrent_6a7fa832-bffa-4960-b3df-185bf5ec8cde_terseLabel_en-US" xlink:label="lab_us-gaap_DisposalGroupIncludingDiscontinuedOperationAssetsNoncurrent" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Disposal Group, Including Discontinued Operation, Assets, Noncurrent, Total</link:label>
    <link:label id="lab_us-gaap_DisposalGroupIncludingDiscontinuedOperationAssetsNoncurrent_label_en-US" xlink:label="lab_us-gaap_DisposalGroupIncludingDiscontinuedOperationAssetsNoncurrent" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Disposal Group, Including Discontinued Operation, Assets, Noncurrent</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DisposalGroupIncludingDiscontinuedOperationAssetsNoncurrent" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_DisposalGroupIncludingDiscontinuedOperationAssetsNoncurrent"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DisposalGroupIncludingDiscontinuedOperationAssetsNoncurrent" xlink:to="lab_us-gaap_DisposalGroupIncludingDiscontinuedOperationAssetsNoncurrent" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_Goodwill_84d484ce-03f2-4c79-83c1-21211893efbc_terseLabel_en-US" xlink:label="lab_us-gaap_Goodwill" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Goodwill</link:label>
    <link:label id="lab_us-gaap_Goodwill_b527259e-742e-4d39-a8b1-7554db2421c1_periodStartLabel_en-US" xlink:label="lab_us-gaap_Goodwill" xlink:role="http://www.xbrl.org/2003/role/periodStartLabel" xlink:type="resource" xml:lang="en-US">Goodwill</link:label>
    <link:label id="lab_us-gaap_Goodwill_643dfd1b-2e52-40d5-9ee3-4ca34840651a_periodEndLabel_en-US" xlink:label="lab_us-gaap_Goodwill" xlink:role="http://www.xbrl.org/2003/role/periodEndLabel" xlink:type="resource" xml:lang="en-US">Goodwill</link:label>
    <link:label id="lab_us-gaap_Goodwill_5de002d4-1822-4aba-95e2-78c3318f9b1f_totalLabel_en-US" xlink:label="lab_us-gaap_Goodwill" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Goodwill - net carrying amount</link:label>
    <link:label id="lab_us-gaap_Goodwill_label_en-US" xlink:label="lab_us-gaap_Goodwill" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Goodwill</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_Goodwill" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_Goodwill"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_Goodwill" xlink:to="lab_us-gaap_Goodwill" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AllowanceForDoubtfulAccountsReceivable_ff353db3-6379-479a-8fed-8ef883f0d9de_terseLabel_en-US" xlink:label="lab_us-gaap_AllowanceForDoubtfulAccountsReceivable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Accounts Receivable, Allowance for Credit Loss</link:label>
    <link:label id="lab_us-gaap_AllowanceForDoubtfulAccountsReceivable_label_en-US" xlink:label="lab_us-gaap_AllowanceForDoubtfulAccountsReceivable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Accounts Receivable, Allowance for Credit Loss</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AllowanceForDoubtfulAccountsReceivable" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_AllowanceForDoubtfulAccountsReceivable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AllowanceForDoubtfulAccountsReceivable" xlink:to="lab_us-gaap_AllowanceForDoubtfulAccountsReceivable" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OtherComprehensiveIncomeLossNetOfTaxPeriodIncreaseDecreaseAbstract_f2e61c6c-f088-40e8-a487-c4a1e77259da_terseLabel_en-US" xlink:label="lab_us-gaap_OtherComprehensiveIncomeLossNetOfTaxPeriodIncreaseDecreaseAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Other comprehensive income (loss)</link:label>
    <link:label id="lab_us-gaap_OtherComprehensiveIncomeLossNetOfTaxPeriodIncreaseDecreaseAbstract_label_en-US" xlink:label="lab_us-gaap_OtherComprehensiveIncomeLossNetOfTaxPeriodIncreaseDecreaseAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Other Comprehensive Income (Loss), Net of Tax [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OtherComprehensiveIncomeLossNetOfTaxPeriodIncreaseDecreaseAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_OtherComprehensiveIncomeLossNetOfTaxPeriodIncreaseDecreaseAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OtherComprehensiveIncomeLossNetOfTaxPeriodIncreaseDecreaseAbstract" xlink:to="lab_us-gaap_OtherComprehensiveIncomeLossNetOfTaxPeriodIncreaseDecreaseAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_codi_ManagementServiceAgreementWithCgmMember_1c07c43a-cd32-4da1-be13-ef18b0c38e05_terseLabel_en-US" xlink:label="lab_codi_ManagementServiceAgreementWithCgmMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Management Service Agreement with CGM</link:label>
    <link:label id="lab_codi_ManagementServiceAgreementWithCgmMember_label_en-US" xlink:label="lab_codi_ManagementServiceAgreementWithCgmMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Management Service Agreement With Cgm [Member]</link:label>
    <link:label id="lab_codi_ManagementServiceAgreementWithCgmMember_documentation_en-US" xlink:label="lab_codi_ManagementServiceAgreementWithCgmMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Management service agreement with CGM.</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_codi_ManagementServiceAgreementWithCgmMember" xlink:href="codi-20241231.xsd#codi_ManagementServiceAgreementWithCgmMember"/>
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    <link:label id="lab_srt_StockRepurchaseProgramAuthorizedAmount1_17aa8fde-7b0e-4fbc-9aad-aa75f45b271e_terseLabel_en-US" xlink:label="lab_srt_StockRepurchaseProgramAuthorizedAmount1" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Share Repurchase Program, Authorized, Amount</link:label>
    <link:label id="lab_srt_StockRepurchaseProgramAuthorizedAmount1_label_en-US" xlink:label="lab_srt_StockRepurchaseProgramAuthorizedAmount1" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Share Repurchase Program, Authorized, Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_srt_StockRepurchaseProgramAuthorizedAmount1" xlink:href="https://xbrl.fasb.org/srt/2024/elts/srt-2024.xsd#srt_StockRepurchaseProgramAuthorizedAmount1"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_srt_StockRepurchaseProgramAuthorizedAmount1" xlink:to="lab_srt_StockRepurchaseProgramAuthorizedAmount1" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_PreferredStockRedemptionPricePerShare_b7d9dcd3-7aee-4e34-a625-5efdb78b4285_terseLabel_en-US" xlink:label="lab_us-gaap_PreferredStockRedemptionPricePerShare" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Preferred Stock, Redemption Price Per Share</link:label>
    <link:label id="lab_us-gaap_PreferredStockRedemptionPricePerShare_label_en-US" xlink:label="lab_us-gaap_PreferredStockRedemptionPricePerShare" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Preferred Stock, Redemption Price Per Share</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PreferredStockRedemptionPricePerShare" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_PreferredStockRedemptionPricePerShare"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PreferredStockRedemptionPricePerShare" xlink:to="lab_us-gaap_PreferredStockRedemptionPricePerShare" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_NoncontrollingInterestIncreaseFromBusinessCombination_bf235e88-1775-47f8-a80e-a3ab22b592ba_terseLabel_en-US" xlink:label="lab_us-gaap_NoncontrollingInterestIncreaseFromBusinessCombination" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Proceeds from noncontrolling interest holders</link:label>
    <link:label id="lab_us-gaap_NoncontrollingInterestIncreaseFromBusinessCombination_label_en-US" xlink:label="lab_us-gaap_NoncontrollingInterestIncreaseFromBusinessCombination" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Noncontrolling Interest, Increase from Business Combination</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_NoncontrollingInterestIncreaseFromBusinessCombination" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_NoncontrollingInterestIncreaseFromBusinessCombination"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_NoncontrollingInterestIncreaseFromBusinessCombination" xlink:to="lab_us-gaap_NoncontrollingInterestIncreaseFromBusinessCombination" xlink:type="arc" order="1"/>
    <link:label id="lab_codi_AciMember_900413fc-3a16-47d2-bf74-82e74c3eabfb_terseLabel_en-US" xlink:label="lab_codi_AciMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Aci [Member]</link:label>
    <link:label id="lab_codi_AciMember_label_en-US" xlink:label="lab_codi_AciMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Aci [Member]</link:label>
    <link:label id="lab_codi_AciMember_documentation_en-US" xlink:label="lab_codi_AciMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">ACI.</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_codi_AciMember" xlink:href="codi-20241231.xsd#codi_AciMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_codi_AciMember" xlink:to="lab_codi_AciMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FairValueAssetsMeasuredOnNonrecurringBasisTextBlock_464aa736-71c8-4e88-b7f8-d2786d1af0db_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueAssetsMeasuredOnNonrecurringBasisTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Summary of Assets and Liabilities Carried at Fair Value Measured on Non-recurring Basis</link:label>
    <link:label id="lab_us-gaap_FairValueAssetsMeasuredOnNonrecurringBasisTextBlock_label_en-US" xlink:label="lab_us-gaap_FairValueAssetsMeasuredOnNonrecurringBasisTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fair Value Measurements, Nonrecurring [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueAssetsMeasuredOnNonrecurringBasisTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_FairValueAssetsMeasuredOnNonrecurringBasisTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FairValueAssetsMeasuredOnNonrecurringBasisTextBlock" xlink:to="lab_us-gaap_FairValueAssetsMeasuredOnNonrecurringBasisTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FixedIncomeSecuritiesMember_8709abb1-ac7a-43b2-8d66-34375046abca_terseLabel_en-US" xlink:label="lab_us-gaap_FixedIncomeSecuritiesMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Fixed Income Securities [Member]</link:label>
    <link:label id="lab_us-gaap_FixedIncomeSecuritiesMember_label_en-US" xlink:label="lab_us-gaap_FixedIncomeSecuritiesMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fixed Income Securities [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FixedIncomeSecuritiesMember" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_FixedIncomeSecuritiesMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FixedIncomeSecuritiesMember" xlink:to="lab_us-gaap_FixedIncomeSecuritiesMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_EmployeeStockOptionMember_terseLabel_en-US" xlink:label="lab_us-gaap_EmployeeStockOptionMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Employee Stock Option</link:label>
    <link:label id="lab_us-gaap_EmployeeStockOptionMember_label_en-US" xlink:label="lab_us-gaap_EmployeeStockOptionMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Share-Based Payment Arrangement, Option [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_EmployeeStockOptionMember" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_EmployeeStockOptionMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_EmployeeStockOptionMember" xlink:to="lab_us-gaap_EmployeeStockOptionMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ReconciliationOfRevenueFromSegmentsToConsolidatedTable_92d69d0e-c872-4000-93d7-47b865830fb1_terseLabel_en-US" xlink:label="lab_us-gaap_ReconciliationOfRevenueFromSegmentsToConsolidatedTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Reconciliation of Revenue from Segments to Consolidated [Table]</link:label>
    <link:label id="lab_us-gaap_ReconciliationOfRevenueFromSegmentsToConsolidatedTable_label_en-US" xlink:label="lab_us-gaap_ReconciliationOfRevenueFromSegmentsToConsolidatedTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Reconciliation of Revenue from Segments to Consolidated [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ReconciliationOfRevenueFromSegmentsToConsolidatedTable" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_ReconciliationOfRevenueFromSegmentsToConsolidatedTable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ReconciliationOfRevenueFromSegmentsToConsolidatedTable" xlink:to="lab_us-gaap_ReconciliationOfRevenueFromSegmentsToConsolidatedTable" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_Depreciation_a3e2a761-6325-4312-a522-6e553f71b804_terseLabel_en-US" xlink:label="lab_us-gaap_Depreciation" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Depreciation expense</link:label>
    <link:label id="lab_us-gaap_Depreciation_label_en-US" xlink:label="lab_us-gaap_Depreciation" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Depreciation</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_Depreciation" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_Depreciation"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_Depreciation" xlink:to="lab_us-gaap_Depreciation" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueNextTwelveMonths_68280011-553b-4e08-84e0-68d787c1a60d_terseLabel_en-US" xlink:label="lab_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueNextTwelveMonths" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">2020</link:label>
    <link:label id="lab_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueNextTwelveMonths_label_en-US" xlink:label="lab_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueNextTwelveMonths" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Lessee, Operating Lease, Liability, to be Paid, Year One</link:label>
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    <link:label id="lab_us-gaap_ProceedsFromPaymentsForOtherFinancingActivities_bdf128f5-bd50-4463-8ff3-0ba184168cca_terseLabel_en-US" xlink:label="lab_us-gaap_ProceedsFromPaymentsForOtherFinancingActivities" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Other</link:label>
    <link:label id="lab_us-gaap_ProceedsFromPaymentsForOtherFinancingActivities_label_en-US" xlink:label="lab_us-gaap_ProceedsFromPaymentsForOtherFinancingActivities" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Proceeds from (Payments for) Other Financing Activities</link:label>
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    <link:label id="lab_codi_DeferredTaxLiabilityRepatriationofForeignEarnings_documentation_en-US" xlink:label="lab_codi_DeferredTaxLiabilityRepatriationofForeignEarnings" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Deferred Tax Liability, Repatriation of Foreign Earnings</link:label>
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    <link:label id="lab_us-gaap_NoncontrollingInterestIncreaseFromSaleOfParentEquityInterest_c17e97a8-95f9-4a97-8060-a0996f08d650_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_NoncontrollingInterestIncreaseFromSaleOfParentEquityInterest" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Effect of FOX IPO proceeds</link:label>
    <link:label id="lab_us-gaap_NoncontrollingInterestIncreaseFromSaleOfParentEquityInterest_label_en-US" xlink:label="lab_us-gaap_NoncontrollingInterestIncreaseFromSaleOfParentEquityInterest" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Noncontrolling Interest, Increase from Sale of Parent Equity Interest</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_NoncontrollingInterestIncreaseFromSaleOfParentEquityInterest" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_NoncontrollingInterestIncreaseFromSaleOfParentEquityInterest"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_NoncontrollingInterestIncreaseFromSaleOfParentEquityInterest" xlink:to="lab_us-gaap_NoncontrollingInterestIncreaseFromSaleOfParentEquityInterest" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ComprehensiveIncomeNetOfTax_d40ec8c0-092e-4180-82c6-15d5142f8c80_totalLabel_en-US" xlink:label="lab_us-gaap_ComprehensiveIncomeNetOfTax" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Total comprehensive income attributable to Holdings, net of tax</link:label>
    <link:label id="lab_us-gaap_ComprehensiveIncomeNetOfTax_label_en-US" xlink:label="lab_us-gaap_ComprehensiveIncomeNetOfTax" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Comprehensive Income (Loss), Net of Tax, Attributable to Parent</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ComprehensiveIncomeNetOfTax" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_ComprehensiveIncomeNetOfTax"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ComprehensiveIncomeNetOfTax" xlink:to="lab_us-gaap_ComprehensiveIncomeNetOfTax" xlink:type="arc" order="1"/>
    <link:label id="lab_codi_SeriesBPreferredSharesRepresentingSeriesBTrustPreferredInterestInCompassDiversifiedHoldingsMember_d15c86b8-8922-4eef-bb92-5e8892e7291d_terseLabel_en-US" xlink:label="lab_codi_SeriesBPreferredSharesRepresentingSeriesBTrustPreferredInterestInCompassDiversifiedHoldingsMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Series B Preferred Shares Representing Series B Trust Preferred Interest In Compass Diversified Holdings [Member]</link:label>
    <link:label id="lab_codi_SeriesBPreferredSharesRepresentingSeriesBTrustPreferredInterestInCompassDiversifiedHoldingsMember_label_en-US" xlink:label="lab_codi_SeriesBPreferredSharesRepresentingSeriesBTrustPreferredInterestInCompassDiversifiedHoldingsMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Series B Preferred Shares Representing Series B Trust Preferred Interest In Compass Diversified Holdings [Member]</link:label>
    <link:label id="lab_codi_SeriesBPreferredSharesRepresentingSeriesBTrustPreferredInterestInCompassDiversifiedHoldingsMember_documentation_en-US" xlink:label="lab_codi_SeriesBPreferredSharesRepresentingSeriesBTrustPreferredInterestInCompassDiversifiedHoldingsMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Series B Preferred Shares Representing Series B Trust Preferred Interest In Compass Diversified Holdings [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_codi_SeriesBPreferredSharesRepresentingSeriesBTrustPreferredInterestInCompassDiversifiedHoldingsMember" xlink:href="codi-20241231.xsd#codi_SeriesBPreferredSharesRepresentingSeriesBTrustPreferredInterestInCompassDiversifiedHoldingsMember"/>
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    <link:label id="lab_us-gaap_AccruedIncomeTaxesCurrent_27210a14-1760-490b-b70c-90c71986303b_terseLabel_en-US" xlink:label="lab_us-gaap_AccruedIncomeTaxesCurrent" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Income taxes payable</link:label>
    <link:label id="lab_us-gaap_AccruedIncomeTaxesCurrent_label_en-US" xlink:label="lab_us-gaap_AccruedIncomeTaxesCurrent" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Accrued Income Taxes, Current</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AccruedIncomeTaxesCurrent" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_AccruedIncomeTaxesCurrent"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AccruedIncomeTaxesCurrent" xlink:to="lab_us-gaap_AccruedIncomeTaxesCurrent" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_PensionPlansDefinedBenefitMember_f4fb1daa-38e7-45c8-be49-e45b3958f190_terseLabel_en-US" xlink:label="lab_us-gaap_PensionPlansDefinedBenefitMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Pension Plan</link:label>
    <link:label id="lab_us-gaap_PensionPlansDefinedBenefitMember_label_en-US" xlink:label="lab_us-gaap_PensionPlansDefinedBenefitMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Pension Plan [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PensionPlansDefinedBenefitMember" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_PensionPlansDefinedBenefitMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PensionPlansDefinedBenefitMember" xlink:to="lab_us-gaap_PensionPlansDefinedBenefitMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FinanceLeaseWeightedAverageDiscountRatePercent_f493bb9b-4ce0-4da6-a2a6-89a55b127f66_terseLabel_en-US" xlink:label="lab_us-gaap_FinanceLeaseWeightedAverageDiscountRatePercent" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Finance Lease, Weighted Average Discount Rate, Percent</link:label>
    <link:label id="lab_us-gaap_FinanceLeaseWeightedAverageDiscountRatePercent_label_en-US" xlink:label="lab_us-gaap_FinanceLeaseWeightedAverageDiscountRatePercent" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Finance Lease, Weighted Average Discount Rate, Percent</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FinanceLeaseWeightedAverageDiscountRatePercent" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_FinanceLeaseWeightedAverageDiscountRatePercent"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FinanceLeaseWeightedAverageDiscountRatePercent" xlink:to="lab_us-gaap_FinanceLeaseWeightedAverageDiscountRatePercent" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_EffectiveIncomeTaxRateReconciliationOtherAdjustments_faebd76b-3962-4bdc-af2e-098f560a7063_terseLabel_en-US" xlink:label="lab_us-gaap_EffectiveIncomeTaxRateReconciliationOtherAdjustments" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Other</link:label>
    <link:label id="lab_us-gaap_EffectiveIncomeTaxRateReconciliationOtherAdjustments_label_en-US" xlink:label="lab_us-gaap_EffectiveIncomeTaxRateReconciliationOtherAdjustments" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Effective Income Tax Rate Reconciliation, Other Adjustments, Percent</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_EffectiveIncomeTaxRateReconciliationOtherAdjustments" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_EffectiveIncomeTaxRateReconciliationOtherAdjustments"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_EffectiveIncomeTaxRateReconciliationOtherAdjustments" xlink:to="lab_us-gaap_EffectiveIncomeTaxRateReconciliationOtherAdjustments" xlink:type="arc" order="1"/>
    <link:label id="lab_codi_FiniteLivedInProcessResearchAndDevelopment_3f146629-4f2e-444e-abb7-5b82aea15dc9_terseLabel_en-US" xlink:label="lab_codi_FiniteLivedInProcessResearchAndDevelopment" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Finite lived in-process research and development</link:label>
    <link:label id="lab_codi_FiniteLivedInProcessResearchAndDevelopment_label_en-US" xlink:label="lab_codi_FiniteLivedInProcessResearchAndDevelopment" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Finite lived in-process research and development</link:label>
    <link:label id="lab_codi_FiniteLivedInProcessResearchAndDevelopment_documentation_en-US" xlink:label="lab_codi_FiniteLivedInProcessResearchAndDevelopment" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Finite lived in-process research and development</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_codi_FiniteLivedInProcessResearchAndDevelopment" xlink:href="codi-20241231.xsd#codi_FiniteLivedInProcessResearchAndDevelopment"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_codi_FiniteLivedInProcessResearchAndDevelopment" xlink:to="lab_codi_FiniteLivedInProcessResearchAndDevelopment" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FinanceLeaseLiabilityPaymentsDueNextTwelveMonths_c0742207-4af9-45ce-bbb3-3a1fa1d2fda1_terseLabel_en-US" xlink:label="lab_us-gaap_FinanceLeaseLiabilityPaymentsDueNextTwelveMonths" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Finance Lease, Liability, to be Paid, Year One</link:label>
    <link:label id="lab_us-gaap_FinanceLeaseLiabilityPaymentsDueNextTwelveMonths_label_en-US" xlink:label="lab_us-gaap_FinanceLeaseLiabilityPaymentsDueNextTwelveMonths" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Finance Lease, Liability, to be Paid, Year One</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FinanceLeaseLiabilityPaymentsDueNextTwelveMonths" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_FinanceLeaseLiabilityPaymentsDueNextTwelveMonths"/>
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    <link:label id="lab_us-gaap_AwardTypeAxis_ea6ca31c-05f3-404c-a0ea-40d3b387bd63_terseLabel_en-US" xlink:label="lab_us-gaap_AwardTypeAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Award Type [Axis]</link:label>
    <link:label id="lab_us-gaap_AwardTypeAxis_label_en-US" xlink:label="lab_us-gaap_AwardTypeAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Award Type [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AwardTypeAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_AwardTypeAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AwardTypeAxis" xlink:to="lab_us-gaap_AwardTypeAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DeferredTaxLiabilities_1e708639-a847-4659-bc9f-86bf761e0705_negatedTotalLabel_en-US" xlink:label="lab_us-gaap_DeferredTaxLiabilities" xlink:role="http://www.xbrl.org/2009/role/negatedTotalLabel" xlink:type="resource" xml:lang="en-US">Total net deferred tax liability</link:label>
    <link:label id="lab_us-gaap_DeferredTaxLiabilities_label_en-US" xlink:label="lab_us-gaap_DeferredTaxLiabilities" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Deferred Tax Liabilities, Net</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DeferredTaxLiabilities" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_DeferredTaxLiabilities"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DeferredTaxLiabilities" xlink:to="lab_us-gaap_DeferredTaxLiabilities" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_InventoryGross_e2453fb8-380a-4161-bc19-e64c8d7bc267_terseLabel_en-US" xlink:label="lab_us-gaap_InventoryGross" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Inventory, Gross</link:label>
    <link:label id="lab_us-gaap_InventoryGross_label_en-US" xlink:label="lab_us-gaap_InventoryGross" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Inventory, Gross</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_InventoryGross" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_InventoryGross"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_InventoryGross" xlink:to="lab_us-gaap_InventoryGross" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_PropertyPlantAndEquipmentNet_c3d8a03f-4735-46c1-b204-5e3db05d328f_verboseLabel_en-US" xlink:label="lab_us-gaap_PropertyPlantAndEquipmentNet" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Property, plant and equipment, net</link:label>
    <link:label id="lab_us-gaap_PropertyPlantAndEquipmentNet_000abe80-d7b5-4060-bc9e-053c0387eb23_terseLabel_en-US" xlink:label="lab_us-gaap_PropertyPlantAndEquipmentNet" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Property, Plant and Equipment, Net</link:label>
    <link:label id="lab_us-gaap_PropertyPlantAndEquipmentNet_713f79bd-a4e6-4b91-8d4b-92c403f397a0_totalLabel_en-US" xlink:label="lab_us-gaap_PropertyPlantAndEquipmentNet" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Total</link:label>
    <link:label id="lab_us-gaap_PropertyPlantAndEquipmentNet_label_en-US" xlink:label="lab_us-gaap_PropertyPlantAndEquipmentNet" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Property, Plant and Equipment, Net</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PropertyPlantAndEquipmentNet" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_PropertyPlantAndEquipmentNet"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PropertyPlantAndEquipmentNet" xlink:to="lab_us-gaap_PropertyPlantAndEquipmentNet" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_IcfrAuditorAttestationFlag_7d09003e-f329-4373-be1a-90faf9885418_terseLabel_en-US" xlink:label="lab_dei_IcfrAuditorAttestationFlag" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">ICFR Auditor Attestation Flag</link:label>
    <link:label id="lab_dei_IcfrAuditorAttestationFlag_label_en-US" xlink:label="lab_dei_IcfrAuditorAttestationFlag" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">ICFR Auditor Attestation Flag</link:label>
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    <link:label id="lab_us-gaap_Liabilities_9ddced92-ac5d-47e9-983d-7aa043996724_totalLabel_en-US" xlink:label="lab_us-gaap_Liabilities" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Total liabilities</link:label>
    <link:label id="lab_us-gaap_Liabilities_label_en-US" xlink:label="lab_us-gaap_Liabilities" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Liabilities</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_Liabilities" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_Liabilities"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_Liabilities" xlink:to="lab_us-gaap_Liabilities" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_MinorityInterest_00716749-c6c1-43cb-82b8-fbcadfbb6fb1_terseLabel_en-US" xlink:label="lab_us-gaap_MinorityInterest" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Noncontrolling interest</link:label>
    <link:label id="lab_us-gaap_MinorityInterest_cb7b0c93-c9ae-4960-bf0a-c19e41b79d21_verboseLabel_en-US" xlink:label="lab_us-gaap_MinorityInterest" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Stockholders' Equity Attributable to Noncontrolling Interest</link:label>
    <link:label id="lab_us-gaap_MinorityInterest_457a18bb-d79f-4681-9b95-92e9dfc6c7b7_netLabel_en-US" xlink:label="lab_us-gaap_MinorityInterest" xlink:role="http://www.xbrl.org/2009/role/netLabel" xlink:type="resource" xml:lang="en-US">Stockholders' Equity Attributable to Noncontrolling Interest</link:label>
    <link:label id="lab_us-gaap_MinorityInterest_label_en-US" xlink:label="lab_us-gaap_MinorityInterest" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Equity, Attributable to Noncontrolling Interest</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_MinorityInterest" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_MinorityInterest"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_MinorityInterest" xlink:to="lab_us-gaap_MinorityInterest" xlink:type="arc" order="1"/>
    <link:label id="lab_codi_AnnualInternalRateOfReturn_feff70ec-390d-4f92-a04e-88f0fa24a553_terseLabel_en-US" xlink:label="lab_codi_AnnualInternalRateOfReturn" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Annual Internal Rate of Return</link:label>
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    <link:label id="lab_codi_AnnualInternalRateOfReturn_documentation_en-US" xlink:label="lab_codi_AnnualInternalRateOfReturn" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Annual Internal Rate of Return</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_codi_AnnualInternalRateOfReturn" xlink:href="codi-20241231.xsd#codi_AnnualInternalRateOfReturn"/>
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    <link:label id="lab_us-gaap_AcquiredFiniteLivedIntangibleAssetsWeightedAverageUsefulLife_5ae38e14-103a-445f-a474-f274e2cc9567_terseLabel_en-US" xlink:label="lab_us-gaap_AcquiredFiniteLivedIntangibleAssetsWeightedAverageUsefulLife" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Intangible assets, estimated useful life</link:label>
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    <link:label id="lab_us-gaap_ForeignCurrencyTransactionsAndTranslationsPolicyTextBlock_13ca8eb0-22ce-4bbc-b0e0-44de010acadc_terseLabel_en-US" xlink:label="lab_us-gaap_ForeignCurrencyTransactionsAndTranslationsPolicyTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Foreign Currency</link:label>
    <link:label id="lab_us-gaap_ForeignCurrencyTransactionsAndTranslationsPolicyTextBlock_label_en-US" xlink:label="lab_us-gaap_ForeignCurrencyTransactionsAndTranslationsPolicyTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Foreign Currency Transactions and Translations Policy [Policy Text Block]</link:label>
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    <link:label id="lab_us-gaap_RevolvingCreditFacilityMember_0cf750fc-4e62-40ff-9b5c-e314830129e9_terseLabel_en-US" xlink:label="lab_us-gaap_RevolvingCreditFacilityMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Revolving Credit Facility</link:label>
    <link:label id="lab_us-gaap_RevolvingCreditFacilityMember_label_en-US" xlink:label="lab_us-gaap_RevolvingCreditFacilityMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Revolving Credit Facility [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_RevolvingCreditFacilityMember" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_RevolvingCreditFacilityMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_RevolvingCreditFacilityMember" xlink:to="lab_us-gaap_RevolvingCreditFacilityMember" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_TrdArrExpirationDate_terseLabel_en-US" xlink:label="lab_ecd_TrdArrExpirationDate" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Expiration Date</link:label>
    <link:label id="lab_ecd_TrdArrExpirationDate_label_en-US" xlink:label="lab_ecd_TrdArrExpirationDate" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Trading Arrangement Expiration Date</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_TrdArrExpirationDate" xlink:href="https://xbrl.sec.gov/ecd/2024/ecd-2024.xsd#ecd_TrdArrExpirationDate"/>
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    <link:label id="lab_us-gaap_NetCashProvidedByUsedInInvestingActivitiesAbstract_da0369e7-a0f5-420b-9d85-98b3c33939e5_terseLabel_en-US" xlink:label="lab_us-gaap_NetCashProvidedByUsedInInvestingActivitiesAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Net Cash Provided by (Used in) Investing Activities [Abstract]</link:label>
    <link:label id="lab_us-gaap_NetCashProvidedByUsedInInvestingActivitiesAbstract_label_en-US" xlink:label="lab_us-gaap_NetCashProvidedByUsedInInvestingActivitiesAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Net Cash Provided by (Used in) Investing Activities [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_NetCashProvidedByUsedInInvestingActivitiesAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_NetCashProvidedByUsedInInvestingActivitiesAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_NetCashProvidedByUsedInInvestingActivitiesAbstract" xlink:to="lab_us-gaap_NetCashProvidedByUsedInInvestingActivitiesAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_NetCashProvidedByUsedInOperatingActivitiesContinuingOperations_c391a688-3dc1-4467-8868-e5934a5e8a48_totalLabel_en-US" xlink:label="lab_us-gaap_NetCashProvidedByUsedInOperatingActivitiesContinuingOperations" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Net cash provided by (used in) operating activities - continuing operations</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_NetCashProvidedByUsedInOperatingActivitiesContinuingOperations" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_NetCashProvidedByUsedInOperatingActivitiesContinuingOperations"/>
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    <link:label id="lab_ecd_TotalShareholderRtnAmt_terseLabel_en-US" xlink:label="lab_ecd_TotalShareholderRtnAmt" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Total Shareholder Return Amount</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_ecd_TotalShareholderRtnAmt" xlink:href="https://xbrl.sec.gov/ecd/2024/ecd-2024.xsd#ecd_TotalShareholderRtnAmt"/>
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    <link:label id="lab_codi_NumberofRelatedPartyVendors_label_en-US" xlink:label="lab_codi_NumberofRelatedPartyVendors" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Number of Related Party Vendors</link:label>
    <link:label id="lab_codi_NumberofRelatedPartyVendors_documentation_en-US" xlink:label="lab_codi_NumberofRelatedPartyVendors" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Number of Related Party Vendors</link:label>
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    <link:label id="lab_codi_LeaseRightOfUseAsset_5f5a56c9-071b-46c8-83e5-998ac8663180_terseLabel_en-US" xlink:label="lab_codi_LeaseRightOfUseAsset" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Lease, Right-of-Use Asset</link:label>
    <link:label id="lab_codi_LeaseRightOfUseAsset_label_en-US" xlink:label="lab_codi_LeaseRightOfUseAsset" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Lease, Right-of-Use Asset</link:label>
    <link:label id="lab_codi_LeaseRightOfUseAsset_documentation_en-US" xlink:label="lab_codi_LeaseRightOfUseAsset" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Lease, Right-of-Use Asset</link:label>
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    <link:label id="lab_us-gaap_DeferredTaxAssetsOperatingLossCarryforwards_7092d5c4-98a0-4998-9dae-4c5c82946def_terseLabel_en-US" xlink:label="lab_us-gaap_DeferredTaxAssetsOperatingLossCarryforwards" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Net operating loss carryforwards</link:label>
    <link:label id="lab_us-gaap_DeferredTaxAssetsOperatingLossCarryforwards_label_en-US" xlink:label="lab_us-gaap_DeferredTaxAssetsOperatingLossCarryforwards" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Deferred Tax Assets, Operating Loss Carryforwards</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DeferredTaxAssetsOperatingLossCarryforwards" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_DeferredTaxAssetsOperatingLossCarryforwards"/>
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    <link:label id="lab_codi_BusinessAcquisitionsDistributionsPayableAllocationAgreementPeriod_9583afe4-7eb5-4557-8af5-07cf307502c5_terseLabel_en-US" xlink:label="lab_codi_BusinessAcquisitionsDistributionsPayableAllocationAgreementPeriod" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Period to acquired controlling interest in business on fifth anniversary</link:label>
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    <link:label id="lab_us-gaap_InventoryRawMaterialsAndSupplies_7eefb754-6dfc-4978-b87e-fe275b2dd450_terseLabel_en-US" xlink:label="lab_us-gaap_InventoryRawMaterialsAndSupplies" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Raw materials and supplies</link:label>
    <link:label id="lab_us-gaap_InventoryRawMaterialsAndSupplies_label_en-US" xlink:label="lab_us-gaap_InventoryRawMaterialsAndSupplies" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Inventory, Raw Materials and Supplies, Gross</link:label>
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    <link:label id="lab_us-gaap_DisposalGroupIncludingDiscontinuedOperationInventoryCurrent_5c110ede-0d9a-4b0e-a323-0c16c5299247_terseLabel_en-US" xlink:label="lab_us-gaap_DisposalGroupIncludingDiscontinuedOperationInventoryCurrent" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Disposal Group, Including Discontinued Operation, Inventory</link:label>
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    <link:label id="lab_codi_EffectiveIncomeTaxRateReconciliationNonRecognitionOfNolCarryForwardsAtSubsidiaries_54e449dd-2367-470f-b6ce-21c8b6ace12e_terseLabel_en-US" xlink:label="lab_codi_EffectiveIncomeTaxRateReconciliationNonRecognitionOfNolCarryForwardsAtSubsidiaries" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Non-recognition of various carryforwards at subsidiaries</link:label>
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    <link:label id="lab_us-gaap_PropertyPlantAndEquipmentGross_dc48d665-32dd-4b0d-a3ca-8ce92f2c9cd5_terseLabel_en-US" xlink:label="lab_us-gaap_PropertyPlantAndEquipmentGross" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Property, plant and equipment, gross</link:label>
    <link:label id="lab_us-gaap_PropertyPlantAndEquipmentGross_label_en-US" xlink:label="lab_us-gaap_PropertyPlantAndEquipmentGross" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Property, Plant and Equipment, Gross</link:label>
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    <link:label id="lab_us-gaap_RetirementPlanNameAxis_e2cea936-f248-4831-bedb-155ed63b1363_terseLabel_en-US" xlink:label="lab_us-gaap_RetirementPlanNameAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Retirement Plan Name [Axis]</link:label>
    <link:label id="lab_us-gaap_RetirementPlanNameAxis_label_en-US" xlink:label="lab_us-gaap_RetirementPlanNameAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Retirement Plan Name [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_RetirementPlanNameAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_RetirementPlanNameAxis"/>
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    <link:label id="lab_us-gaap_DebtInstrumentLineItems_5c9a3eda-e5d8-4167-bc12-db22de2c8029_terseLabel_en-US" xlink:label="lab_us-gaap_DebtInstrumentLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Debt Instrument [Line Items]</link:label>
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    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_SellingGeneralAndAdministrativeExpense" xlink:to="lab_us-gaap_SellingGeneralAndAdministrativeExpense" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CostOfSalesMember_3eba062b-2ed8-4935-8a10-82d00f8f60b4_terseLabel_en-US" xlink:label="lab_us-gaap_CostOfSalesMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Cost of Sales</link:label>
    <link:label id="lab_us-gaap_CostOfSalesMember_label_en-US" xlink:label="lab_us-gaap_CostOfSalesMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Cost of Sales [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CostOfSalesMember" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_CostOfSalesMember"/>
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    <link:label id="lab_us-gaap_SaleOfStockNameOfTransactionDomain_a8a7f382-f16e-43f2-9f55-bbc686211141_terseLabel_en-US" xlink:label="lab_us-gaap_SaleOfStockNameOfTransactionDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Sale of Stock, Name of Transaction [Domain]</link:label>
    <link:label id="lab_us-gaap_SaleOfStockNameOfTransactionDomain_label_en-US" xlink:label="lab_us-gaap_SaleOfStockNameOfTransactionDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Sale of Stock [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SaleOfStockNameOfTransactionDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_SaleOfStockNameOfTransactionDomain"/>
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    <link:label id="lab_dei_DocumentFiscalPeriodFocus_label_en-US" xlink:label="lab_dei_DocumentFiscalPeriodFocus" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Document Fiscal Period Focus</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_DocumentFiscalPeriodFocus" xlink:href="https://xbrl.sec.gov/dei/2024/dei-2024.xsd#dei_DocumentFiscalPeriodFocus"/>
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    <link:label id="lab_us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInYearFour_32d1f038-d8ac-4d30-9040-a876a8b4e4c4_terseLabel_en-US" xlink:label="lab_us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInYearFour" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Long-Term Debt, Maturity, Year Four</link:label>
    <link:label id="lab_us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInYearFour_label_en-US" xlink:label="lab_us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInYearFour" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Long-Term Debt, Maturity, Year Four</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInYearFour" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInYearFour"/>
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    <link:label id="lab_us-gaap_BusinessCombinationAcquisitionRelatedCosts_cf03c63c-8d88-49ef-b80d-9f4784fba785_terseLabel_en-US" xlink:label="lab_us-gaap_BusinessCombinationAcquisitionRelatedCosts" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Business Combination, Acquisition Related Costs</link:label>
    <link:label id="lab_us-gaap_BusinessCombinationAcquisitionRelatedCosts_d8b54b09-b712-42a1-af8c-1f142514d194_verboseLabel_en-US" xlink:label="lab_us-gaap_BusinessCombinationAcquisitionRelatedCosts" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Acquisition-related costs</link:label>
    <link:label id="lab_us-gaap_BusinessCombinationAcquisitionRelatedCosts_label_en-US" xlink:label="lab_us-gaap_BusinessCombinationAcquisitionRelatedCosts" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Business Combination, Acquisition Related Costs</link:label>
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    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_BusinessCombinationAcquisitionRelatedCosts" xlink:to="lab_us-gaap_BusinessCombinationAcquisitionRelatedCosts" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_AllExecutiveCategoriesMember_terseLabel_en-US" xlink:label="lab_ecd_AllExecutiveCategoriesMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">All Executive Categories</link:label>
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    <link:label id="lab_us-gaap_BalanceSheetLocationDomain_e6084482-9295-4e40-8e3b-6253b4ee25d4_terseLabel_en-US" xlink:label="lab_us-gaap_BalanceSheetLocationDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Statement of Financial Position Location, Balance [Domain]</link:label>
    <link:label id="lab_us-gaap_BalanceSheetLocationDomain_label_en-US" xlink:label="lab_us-gaap_BalanceSheetLocationDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Statement of Financial Position Location, Balance [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_BalanceSheetLocationDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_BalanceSheetLocationDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_BalanceSheetLocationDomain" xlink:to="lab_us-gaap_BalanceSheetLocationDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_RetirementPlanTaxStatusDomain_ecf245a4-97f5-499d-912a-bea8362d5cd1_terseLabel_en-US" xlink:label="lab_us-gaap_RetirementPlanTaxStatusDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Retirement Plan Tax Status [Domain]</link:label>
    <link:label id="lab_us-gaap_RetirementPlanTaxStatusDomain_label_en-US" xlink:label="lab_us-gaap_RetirementPlanTaxStatusDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Retirement Plan Tax Status [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_RetirementPlanTaxStatusDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_RetirementPlanTaxStatusDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_RetirementPlanTaxStatusDomain" xlink:to="lab_us-gaap_RetirementPlanTaxStatusDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseYearTwo_ff4a9a53-68ca-4092-8ab8-ce4f112438fd_terseLabel_en-US" xlink:label="lab_us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseYearTwo" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">2021</link:label>
    <link:label id="lab_us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseYearTwo_label_en-US" xlink:label="lab_us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseYearTwo" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Finite-Lived Intangible Asset, Expected Amortization, Year Two</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseYearTwo" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseYearTwo"/>
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    <link:label id="lab_ecd_ChangedPeerGroupFnTextBlock_terseLabel_en-US" xlink:label="lab_ecd_ChangedPeerGroupFnTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Changed Peer Group, Footnote</link:label>
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    <link:label id="lab_us-gaap_BusinessAcquisitionPurchasePriceAllocationGoodwillExpectedTaxDeductibleAmount_57d4906f-2892-486d-9759-c26c5061297e_terseLabel_en-US" xlink:label="lab_us-gaap_BusinessAcquisitionPurchasePriceAllocationGoodwillExpectedTaxDeductibleAmount" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Goodwill deductible for income tax</link:label>
    <link:label id="lab_us-gaap_BusinessAcquisitionPurchasePriceAllocationGoodwillExpectedTaxDeductibleAmount_label_en-US" xlink:label="lab_us-gaap_BusinessAcquisitionPurchasePriceAllocationGoodwillExpectedTaxDeductibleAmount" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Business Acquisition, Goodwill, Expected Tax Deductible Amount</link:label>
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    <link:label id="lab_us-gaap_AssetsAbstract_c43333a1-3ee3-4780-878e-006409cfa816_terseLabel_en-US" xlink:label="lab_us-gaap_AssetsAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Assets</link:label>
    <link:label id="lab_us-gaap_AssetsAbstract_label_en-US" xlink:label="lab_us-gaap_AssetsAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Assets [Abstract]</link:label>
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    <link:label id="lab_codi_BusinessAcquisitionsMember_781d1772-de4b-42fc-a621-c8df744e22f9_terseLabel_en-US" xlink:label="lab_codi_BusinessAcquisitionsMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Business Acquisitions</link:label>
    <link:label id="lab_codi_BusinessAcquisitionsMember_label_en-US" xlink:label="lab_codi_BusinessAcquisitionsMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Business Acquisitions [Member]</link:label>
    <link:label id="lab_codi_BusinessAcquisitionsMember_documentation_en-US" xlink:label="lab_codi_BusinessAcquisitionsMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Business Acquisitions</link:label>
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    <link:label id="lab_us-gaap_RetirementPlanTypeDomain_9945dd6f-182e-405f-a3ac-e7fd1f67d4b5_terseLabel_en-US" xlink:label="lab_us-gaap_RetirementPlanTypeDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Retirement Plan Type [Domain]</link:label>
    <link:label id="lab_us-gaap_RetirementPlanTypeDomain_label_en-US" xlink:label="lab_us-gaap_RetirementPlanTypeDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Retirement Plan Type [Domain]</link:label>
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    <link:label id="lab_us-gaap_OtherComprehensiveIncomeLossNetOfTax_df557325-0cb9-4a62-ac00-7e75732cc7a6_verboseLabel_en-US" xlink:label="lab_us-gaap_OtherComprehensiveIncomeLossNetOfTax" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Total comprehensive income (loss), net</link:label>
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    <link:label id="lab_us-gaap_ProfessionalAndContractServicesExpense_722a7972-eeb9-4c8e-a3bb-52dedac8b601_terseLabel_en-US" xlink:label="lab_us-gaap_ProfessionalAndContractServicesExpense" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Reimbursement of occupancy and staffing costs to CGM</link:label>
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    <link:label id="lab_codi_OptionActivityAttributableToNoncontrollingInterestHolders_3ff663ee-80b2-4570-ace9-347938018c4e_terseLabel_en-US" xlink:label="lab_codi_OptionActivityAttributableToNoncontrollingInterestHolders" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Option activity attributable to noncontrolling shareholders</link:label>
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    <link:label id="lab_codi_OptionActivityAttributableToNoncontrollingInterestHolders_documentation_en-US" xlink:label="lab_codi_OptionActivityAttributableToNoncontrollingInterestHolders" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Stock option activity of noncontrolling interest holders attributable to subsidiary stock.</link:label>
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    <link:label id="lab_us-gaap_ScheduleOfDefinedBenefitPlansDisclosuresTable_f34e21a2-c2a1-49f9-baac-2af0ed6c410a_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfDefinedBenefitPlansDisclosuresTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Defined Benefit Plan [Table]</link:label>
    <link:label id="lab_us-gaap_ScheduleOfDefinedBenefitPlansDisclosuresTable_label_en-US" xlink:label="lab_us-gaap_ScheduleOfDefinedBenefitPlansDisclosuresTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Defined Benefit Plan [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfDefinedBenefitPlansDisclosuresTable" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_ScheduleOfDefinedBenefitPlansDisclosuresTable"/>
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    <link:label id="lab_us-gaap_NetCashProvidedByUsedInDiscontinuedOperations_d26a25d8-b4f2-4222-8496-77cc5258afbb_terseLabel_en-US" xlink:label="lab_us-gaap_NetCashProvidedByUsedInDiscontinuedOperations" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Cash from discontinued operations</link:label>
    <link:label id="lab_us-gaap_NetCashProvidedByUsedInDiscontinuedOperations_label_en-US" xlink:label="lab_us-gaap_NetCashProvidedByUsedInDiscontinuedOperations" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Net Cash Provided by (Used in) Discontinued Operations</link:label>
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    <link:label id="lab_us-gaap_SecuredOvernightFinancingRateSofrOvernightIndexSwapRateMember_09a5cf60-00a7-4492-a03a-f17525d57731_terseLabel_en-US" xlink:label="lab_us-gaap_SecuredOvernightFinancingRateSofrOvernightIndexSwapRateMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Secured Overnight Financing Rate (SOFR) Overnight Index Swap Rate</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SecuredOvernightFinancingRateSofrOvernightIndexSwapRateMember" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_SecuredOvernightFinancingRateSofrOvernightIndexSwapRateMember"/>
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    <link:label id="lab_us-gaap_SubsequentEventTable_e7deff75-968a-459f-aecf-8acb49b7384a_terseLabel_en-US" xlink:label="lab_us-gaap_SubsequentEventTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Subsequent Event [Table]</link:label>
    <link:label id="lab_us-gaap_SubsequentEventTable_label_en-US" xlink:label="lab_us-gaap_SubsequentEventTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Subsequent Event [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SubsequentEventTable" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_SubsequentEventTable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_SubsequentEventTable" xlink:to="lab_us-gaap_SubsequentEventTable" xlink:type="arc" order="1"/>
    <link:label id="lab_srt_MaximumMember_42ddb83e-3009-429d-8bda-11a3dfcb5a76_terseLabel_en-US" xlink:label="lab_srt_MaximumMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Maximum</link:label>
    <link:label id="lab_srt_MaximumMember_label_en-US" xlink:label="lab_srt_MaximumMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Maximum [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_srt_MaximumMember" xlink:href="https://xbrl.fasb.org/srt/2024/elts/srt-2024.xsd#srt_MaximumMember"/>
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    <link:label id="lab_ecd_EquityValuationAssumptionDifferenceFnTextBlock_terseLabel_en-US" xlink:label="lab_ecd_EquityValuationAssumptionDifferenceFnTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Equity Valuation Assumption Difference, Footnote</link:label>
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    <link:label id="lab_us-gaap_GoodwillImpairedAccumulatedImpairmentLoss_096c37e4-f217-4a66-8ba3-a4c8d52322bd_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_GoodwillImpairedAccumulatedImpairmentLoss" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Accumulated impairment losses</link:label>
    <link:label id="lab_us-gaap_GoodwillImpairedAccumulatedImpairmentLoss_29528689-ca9d-45fc-af17-371b318e8e5b_terseLabel_en-US" xlink:label="lab_us-gaap_GoodwillImpairedAccumulatedImpairmentLoss" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Goodwill, impaired, accumulated impairment loss</link:label>
    <link:label id="lab_us-gaap_GoodwillImpairedAccumulatedImpairmentLoss_label_en-US" xlink:label="lab_us-gaap_GoodwillImpairedAccumulatedImpairmentLoss" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Goodwill, Impaired, Accumulated Impairment Loss</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_GoodwillImpairedAccumulatedImpairmentLoss" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_GoodwillImpairedAccumulatedImpairmentLoss"/>
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    <link:label id="lab_us-gaap_FiniteLivedIntangibleAssetsNet_99e3270c-c951-4f42-8b16-2ad1c4813b9b_terseLabel_en-US" xlink:label="lab_us-gaap_FiniteLivedIntangibleAssetsNet" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Carrying value of trade names</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FiniteLivedIntangibleAssetsNet" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_FiniteLivedIntangibleAssetsNet"/>
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    <link:label id="lab_us-gaap_AccountsPayableCurrent_f288ec08-07ee-4c19-b619-7f2cee258b53_terseLabel_en-US" xlink:label="lab_us-gaap_AccountsPayableCurrent" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Accounts payable</link:label>
    <link:label id="lab_us-gaap_AccountsPayableCurrent_label_en-US" xlink:label="lab_us-gaap_AccountsPayableCurrent" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Accounts Payable, Current</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AccountsPayableCurrent" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_AccountsPayableCurrent"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AccountsPayableCurrent" xlink:to="lab_us-gaap_AccountsPayableCurrent" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_SharesIssuedPricePerShare_0490d603-ea56-4c86-a266-aea1206fdb83_terseLabel_en-US" xlink:label="lab_us-gaap_SharesIssuedPricePerShare" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Shares Issued, Price Per Share</link:label>
    <link:label id="lab_us-gaap_SharesIssuedPricePerShare_label_en-US" xlink:label="lab_us-gaap_SharesIssuedPricePerShare" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Shares Issued, Price Per Share</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SharesIssuedPricePerShare" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_SharesIssuedPricePerShare"/>
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    <link:label id="lab_codi_OwnershipPercentageOfTrustInterestHeldByParentEntity_b6f2eeae-5056-4873-a45a-e3f1baf9094b_terseLabel_en-US" xlink:label="lab_codi_OwnershipPercentageOfTrustInterestHeldByParentEntity" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Sole owner of Trust interest of the company</link:label>
    <link:label id="lab_codi_OwnershipPercentageOfTrustInterestHeldByParentEntity_label_en-US" xlink:label="lab_codi_OwnershipPercentageOfTrustInterestHeldByParentEntity" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Ownership Percentage Of Trust Interest Held By Parent Entity</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_codi_OwnershipPercentageOfTrustInterestHeldByParentEntity" xlink:href="codi-20241231.xsd#codi_OwnershipPercentageOfTrustInterestHeldByParentEntity"/>
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    <link:label id="lab_srt_RangeAxis_14d635ac-a5fa-40d8-8b3b-dad84857871a_terseLabel_en-US" xlink:label="lab_srt_RangeAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Statistical Measurement [Axis]</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_srt_RangeAxis" xlink:href="https://xbrl.fasb.org/srt/2024/elts/srt-2024.xsd#srt_RangeAxis"/>
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    <link:label id="lab_us-gaap_PaymentsToMinorityShareholders_11f098ac-4e7e-49e7-b1d7-8a51b6edc56a_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_PaymentsToMinorityShareholders" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Payments to Noncontrolling Interests</link:label>
    <link:label id="lab_us-gaap_PaymentsToMinorityShareholders_3d785223-6ad2-4014-b9bc-dce5a8eae295_terseLabel_en-US" xlink:label="lab_us-gaap_PaymentsToMinorityShareholders" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Payments to Noncontrolling Interests</link:label>
    <link:label id="lab_us-gaap_PaymentsToMinorityShareholders_label_en-US" xlink:label="lab_us-gaap_PaymentsToMinorityShareholders" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Payments to Noncontrolling Interests</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PaymentsToMinorityShareholders" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_PaymentsToMinorityShareholders"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PaymentsToMinorityShareholders" xlink:to="lab_us-gaap_PaymentsToMinorityShareholders" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_IncomeLossFromContinuingOperationsBeforeIncomeTaxesExtraordinaryItemsNoncontrollingInterest_3fc9b68b-c777-408d-87d5-de1e211949cb_totalLabel_en-US" xlink:label="lab_us-gaap_IncomeLossFromContinuingOperationsBeforeIncomeTaxesExtraordinaryItemsNoncontrollingInterest" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Income Before Income Taxes</link:label>
    <link:label id="lab_us-gaap_IncomeLossFromContinuingOperationsBeforeIncomeTaxesExtraordinaryItemsNoncontrollingInterest_e5fd9c37-6cc6-4bfa-8c00-0cbee24c2f68_terseLabel_en-US" xlink:label="lab_us-gaap_IncomeLossFromContinuingOperationsBeforeIncomeTaxesExtraordinaryItemsNoncontrollingInterest" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Income (Loss) from Continuing Operations before Income Taxes, Noncontrolling Interest</link:label>
    <link:label id="lab_us-gaap_IncomeLossFromContinuingOperationsBeforeIncomeTaxesExtraordinaryItemsNoncontrollingInterest_label_en-US" xlink:label="lab_us-gaap_IncomeLossFromContinuingOperationsBeforeIncomeTaxesExtraordinaryItemsNoncontrollingInterest" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Income (Loss) from Continuing Operations before Income Taxes, Noncontrolling Interest</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncomeLossFromContinuingOperationsBeforeIncomeTaxesExtraordinaryItemsNoncontrollingInterest" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_IncomeLossFromContinuingOperationsBeforeIncomeTaxesExtraordinaryItemsNoncontrollingInterest"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_IncomeLossFromContinuingOperationsBeforeIncomeTaxesExtraordinaryItemsNoncontrollingInterest" xlink:to="lab_us-gaap_IncomeLossFromContinuingOperationsBeforeIncomeTaxesExtraordinaryItemsNoncontrollingInterest" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_NonPeoNeoAvgTotalCompAmt_terseLabel_en-US" xlink:label="lab_ecd_NonPeoNeoAvgTotalCompAmt" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Non-PEO NEO Average Total Compensation Amount</link:label>
    <link:label id="lab_ecd_NonPeoNeoAvgTotalCompAmt_label_en-US" xlink:label="lab_ecd_NonPeoNeoAvgTotalCompAmt" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Non-PEO NEO Average Total Compensation Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_NonPeoNeoAvgTotalCompAmt" xlink:href="https://xbrl.sec.gov/ecd/2024/ecd-2024.xsd#ecd_NonPeoNeoAvgTotalCompAmt"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_NonPeoNeoAvgTotalCompAmt" xlink:to="lab_ecd_NonPeoNeoAvgTotalCompAmt" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DeferredTaxLiabilitiesPropertyPlantAndEquipment_c2d8fac8-2651-4e18-b637-7762eb385fec_negatedLabel_en-US" xlink:label="lab_us-gaap_DeferredTaxLiabilitiesPropertyPlantAndEquipment" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:type="resource" xml:lang="en-US">Property and equipment</link:label>
    <link:label id="lab_us-gaap_DeferredTaxLiabilitiesPropertyPlantAndEquipment_label_en-US" xlink:label="lab_us-gaap_DeferredTaxLiabilitiesPropertyPlantAndEquipment" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Deferred Tax Liabilities, Property, Plant and Equipment</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DeferredTaxLiabilitiesPropertyPlantAndEquipment" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_DeferredTaxLiabilitiesPropertyPlantAndEquipment"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DeferredTaxLiabilitiesPropertyPlantAndEquipment" xlink:to="lab_us-gaap_DeferredTaxLiabilitiesPropertyPlantAndEquipment" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_OutstandingRecoveryIndName_terseLabel_en-US" xlink:label="lab_ecd_OutstandingRecoveryIndName" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Name</link:label>
    <link:label id="lab_ecd_OutstandingRecoveryIndName_label_en-US" xlink:label="lab_ecd_OutstandingRecoveryIndName" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Outstanding Recovery, Individual Name</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_OutstandingRecoveryIndName" xlink:href="https://xbrl.sec.gov/ecd/2024/ecd-2024.xsd#ecd_OutstandingRecoveryIndName"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_OutstandingRecoveryIndName" xlink:to="lab_ecd_OutstandingRecoveryIndName" xlink:type="arc" order="1"/>
    <link:label id="lab_codi_OrganizationAndBusinessOperationsTextBlock_312ccb95-f624-4049-bce5-9eca85c56dc1_terseLabel_en-US" xlink:label="lab_codi_OrganizationAndBusinessOperationsTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Organization and Business Operations</link:label>
    <link:label id="lab_codi_OrganizationAndBusinessOperationsTextBlock_label_en-US" xlink:label="lab_codi_OrganizationAndBusinessOperationsTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Organization And Business Operations [Text Block]</link:label>
    <link:label id="lab_codi_OrganizationAndBusinessOperationsTextBlock_documentation_en-US" xlink:label="lab_codi_OrganizationAndBusinessOperationsTextBlock" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">A general description of the company's organization.</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_codi_OrganizationAndBusinessOperationsTextBlock" xlink:href="codi-20241231.xsd#codi_OrganizationAndBusinessOperationsTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_codi_OrganizationAndBusinessOperationsTextBlock" xlink:to="lab_codi_OrganizationAndBusinessOperationsTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DisaggregationOfRevenueLineItems_a86f4300-ec79-4d8f-9eb5-8ff0d008c6ef_terseLabel_en-US" xlink:label="lab_us-gaap_DisaggregationOfRevenueLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Disaggregation of Revenue [Line Items]</link:label>
    <link:label id="lab_us-gaap_DisaggregationOfRevenueLineItems_label_en-US" xlink:label="lab_us-gaap_DisaggregationOfRevenueLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Disaggregation of Revenue [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DisaggregationOfRevenueLineItems" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_DisaggregationOfRevenueLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DisaggregationOfRevenueLineItems" xlink:to="lab_us-gaap_DisaggregationOfRevenueLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ScheduleOfDisposalGroupsIncludingDiscontinuedOperationsIncomeStatementBalanceSheetAndAdditionalDisclosuresTextBlock_68d621a3-126e-4936-a3ff-00bb6ba10113_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfDisposalGroupsIncludingDiscontinuedOperationsIncomeStatementBalanceSheetAndAdditionalDisclosuresTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Disposal Groups, Including Discontinued Operations [Table Text Block]</link:label>
    <link:label id="lab_us-gaap_ScheduleOfDisposalGroupsIncludingDiscontinuedOperationsIncomeStatementBalanceSheetAndAdditionalDisclosuresTextBlock_label_en-US" xlink:label="lab_us-gaap_ScheduleOfDisposalGroupsIncludingDiscontinuedOperationsIncomeStatementBalanceSheetAndAdditionalDisclosuresTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Disposal Groups, Including Discontinued Operations [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfDisposalGroupsIncludingDiscontinuedOperationsIncomeStatementBalanceSheetAndAdditionalDisclosuresTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_ScheduleOfDisposalGroupsIncludingDiscontinuedOperationsIncomeStatementBalanceSheetAndAdditionalDisclosuresTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ScheduleOfDisposalGroupsIncludingDiscontinuedOperationsIncomeStatementBalanceSheetAndAdditionalDisclosuresTextBlock" xlink:to="lab_us-gaap_ScheduleOfDisposalGroupsIncludingDiscontinuedOperationsIncomeStatementBalanceSheetAndAdditionalDisclosuresTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_GoodwillImpairmentLoss_229b3350-d20b-48d6-9907-8d720c891fa6_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_GoodwillImpairmentLoss" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Goodwill impairment expense</link:label>
    <link:label id="lab_us-gaap_GoodwillImpairmentLoss_9b42c4b3-8232-48b6-9e65-aba234e38890_terseLabel_en-US" xlink:label="lab_us-gaap_GoodwillImpairmentLoss" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Goodwill impairment expense</link:label>
    <link:label id="lab_us-gaap_GoodwillImpairmentLoss_label_en-US" xlink:label="lab_us-gaap_GoodwillImpairmentLoss" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Goodwill, Impairment Loss</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_GoodwillImpairmentLoss" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_GoodwillImpairmentLoss"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_GoodwillImpairmentLoss" xlink:to="lab_us-gaap_GoodwillImpairmentLoss" xlink:type="arc" order="1"/>
    <link:label id="lab_srt_TitleOfIndividualAxis_13dc5fd5-101d-4b1a-a397-9b78863a1583_terseLabel_en-US" xlink:label="lab_srt_TitleOfIndividualAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Title and Position [Axis]</link:label>
    <link:label id="lab_srt_TitleOfIndividualAxis_label_en-US" xlink:label="lab_srt_TitleOfIndividualAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Title and Position [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_srt_TitleOfIndividualAxis" xlink:href="https://xbrl.fasb.org/srt/2024/elts/srt-2024.xsd#srt_TitleOfIndividualAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_srt_TitleOfIndividualAxis" xlink:to="lab_srt_TitleOfIndividualAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DisposalGroupIncludingDiscontinuedOperationGoodwill1_09fc4d80-4ca4-412b-bc08-a11a95994d01_terseLabel_en-US" xlink:label="lab_us-gaap_DisposalGroupIncludingDiscontinuedOperationGoodwill1" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Disposal Group, Including Discontinued Operation, Goodwill</link:label>
    <link:label id="lab_us-gaap_DisposalGroupIncludingDiscontinuedOperationGoodwill1_label_en-US" xlink:label="lab_us-gaap_DisposalGroupIncludingDiscontinuedOperationGoodwill1" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Disposal Group, Including Discontinued Operation, Goodwill</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DisposalGroupIncludingDiscontinuedOperationGoodwill1" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_DisposalGroupIncludingDiscontinuedOperationGoodwill1"/>
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    <link:label id="lab_codi_AtTheMarketEquityOfferingCommonMember_b2f14c81-adee-47c2-8f81-16b1067da11d_terseLabel_en-US" xlink:label="lab_codi_AtTheMarketEquityOfferingCommonMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">At the market equity offering</link:label>
    <link:label id="lab_codi_AtTheMarketEquityOfferingCommonMember_label_en-US" xlink:label="lab_codi_AtTheMarketEquityOfferingCommonMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">At the market equity offering - common [Member]</link:label>
    <link:label id="lab_codi_AtTheMarketEquityOfferingCommonMember_documentation_en-US" xlink:label="lab_codi_AtTheMarketEquityOfferingCommonMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">At the market equity offering - common</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_codi_AtTheMarketEquityOfferingCommonMember" xlink:href="codi-20241231.xsd#codi_AtTheMarketEquityOfferingCommonMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_codi_AtTheMarketEquityOfferingCommonMember" xlink:to="lab_codi_AtTheMarketEquityOfferingCommonMember" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_AwardTmgPredtrmndFlag_terseLabel_en-US" xlink:label="lab_ecd_AwardTmgPredtrmndFlag" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Award Timing Predetermined</link:label>
    <link:label id="lab_ecd_AwardTmgPredtrmndFlag_label_en-US" xlink:label="lab_ecd_AwardTmgPredtrmndFlag" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Award Timing Predetermined [Flag]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_AwardTmgPredtrmndFlag" xlink:href="https://xbrl.sec.gov/ecd/2024/ecd-2024.xsd#ecd_AwardTmgPredtrmndFlag"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_AwardTmgPredtrmndFlag" xlink:to="lab_ecd_AwardTmgPredtrmndFlag" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_SubsequentEventTypeDomain_fad72214-e32a-43ab-8e23-f0b66c6b005b_terseLabel_en-US" xlink:label="lab_us-gaap_SubsequentEventTypeDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Subsequent Event Type [Domain]</link:label>
    <link:label id="lab_us-gaap_SubsequentEventTypeDomain_label_en-US" xlink:label="lab_us-gaap_SubsequentEventTypeDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Subsequent Event Type [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SubsequentEventTypeDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_SubsequentEventTypeDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_SubsequentEventTypeDomain" xlink:to="lab_us-gaap_SubsequentEventTypeDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_codi_BeginningBalanceAbstract_9bc77ed3-b920-406b-a3d2-aa63b371f5aa_terseLabel_en-US" xlink:label="lab_codi_BeginningBalanceAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Balance as of January 1, 2014</link:label>
    <link:label id="lab_codi_BeginningBalanceAbstract_label_en-US" xlink:label="lab_codi_BeginningBalanceAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Beginning Balance [Abstract]</link:label>
    <link:label id="lab_codi_BeginningBalanceAbstract_documentation_en-US" xlink:label="lab_codi_BeginningBalanceAbstract" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Beginning balance.</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_codi_BeginningBalanceAbstract" xlink:href="codi-20241231.xsd#codi_BeginningBalanceAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_codi_BeginningBalanceAbstract" xlink:to="lab_codi_BeginningBalanceAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_srt_ScheduleOfEquityMethodInvestmentEquityMethodInvesteeNameAxis_275636dd-5439-4105-9ddd-35bc8270e6e3_terseLabel_en-US" xlink:label="lab_srt_ScheduleOfEquityMethodInvestmentEquityMethodInvesteeNameAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Investment, Name [Axis]</link:label>
    <link:label id="lab_srt_ScheduleOfEquityMethodInvestmentEquityMethodInvesteeNameAxis_label_en-US" xlink:label="lab_srt_ScheduleOfEquityMethodInvestmentEquityMethodInvesteeNameAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Investment, Name [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_srt_ScheduleOfEquityMethodInvestmentEquityMethodInvesteeNameAxis" xlink:href="https://xbrl.fasb.org/srt/2024/elts/srt-2024.xsd#srt_ScheduleOfEquityMethodInvestmentEquityMethodInvesteeNameAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_srt_ScheduleOfEquityMethodInvestmentEquityMethodInvesteeNameAxis" xlink:to="lab_srt_ScheduleOfEquityMethodInvestmentEquityMethodInvesteeNameAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CustomerRelationshipsMember_b1d2d9e0-d8c1-4f19-88f5-411594742187_terseLabel_en-US" xlink:label="lab_us-gaap_CustomerRelationshipsMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Customer relationships</link:label>
    <link:label id="lab_us-gaap_CustomerRelationshipsMember_6e46fbfc-1be8-473a-b65f-8fbca3939137_verboseLabel_en-US" xlink:label="lab_us-gaap_CustomerRelationshipsMember" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Customer relationships</link:label>
    <link:label id="lab_us-gaap_CustomerRelationshipsMember_label_en-US" xlink:label="lab_us-gaap_CustomerRelationshipsMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Customer Relationships [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CustomerRelationshipsMember" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_CustomerRelationshipsMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CustomerRelationshipsMember" xlink:to="lab_us-gaap_CustomerRelationshipsMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_EarningsPerShareDiluted_9dbcff76-3aaf-4a06-a3e1-87aa345889dd_totalLabel_en-US" xlink:label="lab_us-gaap_EarningsPerShareDiluted" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Weighted average number of shares outstanding - basic and fully diluted</link:label>
    <link:label id="lab_us-gaap_EarningsPerShareDiluted_2e28afde-e4f5-4537-a26c-10b294bad79b_terseLabel_en-US" xlink:label="lab_us-gaap_EarningsPerShareDiluted" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Earnings per share, diluted</link:label>
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    <link:label id="lab_us-gaap_IncomeTaxExpenseBenefit_label_en-US" xlink:label="lab_us-gaap_IncomeTaxExpenseBenefit" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Income Tax Expense (Benefit)</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncomeTaxExpenseBenefit" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_IncomeTaxExpenseBenefit"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_IncomeTaxExpenseBenefit" xlink:to="lab_us-gaap_IncomeTaxExpenseBenefit" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DefinedBenefitPlanInterestCost_16120752-27f9-4024-b41e-de6a1c320722_terseLabel_en-US" xlink:label="lab_us-gaap_DefinedBenefitPlanInterestCost" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Interest cost</link:label>
    <link:label id="lab_us-gaap_DefinedBenefitPlanInterestCost_label_en-US" xlink:label="lab_us-gaap_DefinedBenefitPlanInterestCost" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Defined Benefit Plan, Interest Cost</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DefinedBenefitPlanInterestCost" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_DefinedBenefitPlanInterestCost"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DefinedBenefitPlanInterestCost" xlink:to="lab_us-gaap_DefinedBenefitPlanInterestCost" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_NonoperatingIncomeExpenseAbstract_c3829a21-21d8-40e1-8cdd-70ccbb57a08e_terseLabel_en-US" xlink:label="lab_us-gaap_NonoperatingIncomeExpenseAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Other income (expense):</link:label>
    <link:label id="lab_us-gaap_NonoperatingIncomeExpenseAbstract_label_en-US" xlink:label="lab_us-gaap_NonoperatingIncomeExpenseAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Nonoperating Income (Expense) [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_NonoperatingIncomeExpenseAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_NonoperatingIncomeExpenseAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_NonoperatingIncomeExpenseAbstract" xlink:to="lab_us-gaap_NonoperatingIncomeExpenseAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_RevenueFromContractWithCustomerExcludingAssessedTax_842dfc62-7bf0-4ca8-8ce1-cab9398aa81d_terseLabel_en-US" xlink:label="lab_us-gaap_RevenueFromContractWithCustomerExcludingAssessedTax" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Revenue from Contract with Customer, Excluding Assessed Tax</link:label>
    <link:label id="lab_us-gaap_RevenueFromContractWithCustomerExcludingAssessedTax_label_en-US" xlink:label="lab_us-gaap_RevenueFromContractWithCustomerExcludingAssessedTax" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Revenue from Contract with Customer, Excluding Assessed Tax</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_RevenueFromContractWithCustomerExcludingAssessedTax" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_RevenueFromContractWithCustomerExcludingAssessedTax"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_RevenueFromContractWithCustomerExcludingAssessedTax" xlink:to="lab_us-gaap_RevenueFromContractWithCustomerExcludingAssessedTax" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_StatementOfIncomeAndComprehensiveIncomeAbstract_328da90c-3d39-408f-8455-2abafed2f567_terseLabel_en-US" xlink:label="lab_us-gaap_StatementOfIncomeAndComprehensiveIncomeAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Statement of Comprehensive Income [Abstract]</link:label>
    <link:label id="lab_us-gaap_StatementOfIncomeAndComprehensiveIncomeAbstract_label_en-US" xlink:label="lab_us-gaap_StatementOfIncomeAndComprehensiveIncomeAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Statement of Comprehensive Income [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_StatementOfIncomeAndComprehensiveIncomeAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_StatementOfIncomeAndComprehensiveIncomeAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_StatementOfIncomeAndComprehensiveIncomeAbstract" xlink:to="lab_us-gaap_StatementOfIncomeAndComprehensiveIncomeAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FinanceLeaseLiabilityNoncurrentStatementOfFinancialPositionExtensibleList_5cd0c8ee-b05e-4fd2-a684-96df86e79773_terseLabel_en-US" xlink:label="lab_us-gaap_FinanceLeaseLiabilityNoncurrentStatementOfFinancialPositionExtensibleList" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Finance Lease, Liability, Noncurrent, Statement of Financial Position [Extensible Enumeration]</link:label>
    <link:label id="lab_us-gaap_FinanceLeaseLiabilityNoncurrentStatementOfFinancialPositionExtensibleList_label_en-US" xlink:label="lab_us-gaap_FinanceLeaseLiabilityNoncurrentStatementOfFinancialPositionExtensibleList" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Finance Lease, Liability, Noncurrent, Statement of Financial Position [Extensible Enumeration]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FinanceLeaseLiabilityNoncurrentStatementOfFinancialPositionExtensibleList" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_FinanceLeaseLiabilityNoncurrentStatementOfFinancialPositionExtensibleList"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FinanceLeaseLiabilityNoncurrentStatementOfFinancialPositionExtensibleList" xlink:to="lab_us-gaap_FinanceLeaseLiabilityNoncurrentStatementOfFinancialPositionExtensibleList" xlink:type="arc" order="1"/>
    <link:label id="lab_codi_Debtissuanceaggregateprincipalamount_83a02f70-b614-4918-87ee-72725cba72a9_terseLabel_en-US" xlink:label="lab_codi_Debtissuanceaggregateprincipalamount" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Debt issuance, aggregate principal amount</link:label>
    <link:label id="lab_codi_Debtissuanceaggregateprincipalamount_label_en-US" xlink:label="lab_codi_Debtissuanceaggregateprincipalamount" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt issuance, aggregate principal amount</link:label>
    <link:label id="lab_codi_Debtissuanceaggregateprincipalamount_documentation_en-US" xlink:label="lab_codi_Debtissuanceaggregateprincipalamount" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Debt issuance, aggregate principal amount</link:label>
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    <link:label id="lab_codi_LeaseSupplementalBalanceSheetInformationTableTableTextBlock_3d89401c-3152-4eb5-bd7e-5675d3d52175_terseLabel_en-US" xlink:label="lab_codi_LeaseSupplementalBalanceSheetInformationTableTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Lease Supplemental Balance Sheet Information Table</link:label>
    <link:label id="lab_codi_LeaseSupplementalBalanceSheetInformationTableTableTextBlock_label_en-US" xlink:label="lab_codi_LeaseSupplementalBalanceSheetInformationTableTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Lease Supplemental Balance Sheet Information Table [Table Text Block]</link:label>
    <link:label id="lab_codi_LeaseSupplementalBalanceSheetInformationTableTableTextBlock_documentation_en-US" xlink:label="lab_codi_LeaseSupplementalBalanceSheetInformationTableTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Lease Supplemental Balance Sheet Information Table</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_codi_LeaseSupplementalBalanceSheetInformationTableTableTextBlock" xlink:href="codi-20241231.xsd#codi_LeaseSupplementalBalanceSheetInformationTableTableTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_codi_LeaseSupplementalBalanceSheetInformationTableTableTextBlock" xlink:to="lab_codi_LeaseSupplementalBalanceSheetInformationTableTableTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_NetCashProvidedByUsedInInvestingActivities_fedbd63c-536e-4ac5-9c5f-ca3ea152cd37_totalLabel_en-US" xlink:label="lab_us-gaap_NetCashProvidedByUsedInInvestingActivities" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Net cash provided by (used in) investing activities</link:label>
    <link:label id="lab_us-gaap_NetCashProvidedByUsedInInvestingActivities_label_en-US" xlink:label="lab_us-gaap_NetCashProvidedByUsedInInvestingActivities" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Net Cash Provided by (Used in) Investing Activities</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_NetCashProvidedByUsedInInvestingActivities" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_NetCashProvidedByUsedInInvestingActivities"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_NetCashProvidedByUsedInInvestingActivities" xlink:to="lab_us-gaap_NetCashProvidedByUsedInInvestingActivities" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_InterestExpense_31bc5b75-ae88-4b6b-b038-5fedee8de304_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_InterestExpense" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Interest Expense, Operating and Nonoperating</link:label>
    <link:label id="lab_us-gaap_InterestExpense_902a6b72-0157-4ada-9729-b2c00bacf0be_verboseLabel_en-US" xlink:label="lab_us-gaap_InterestExpense" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Interest expense, net</link:label>
    <link:label id="lab_us-gaap_InterestExpense_7464b06d-fbd6-4c35-a864-53593076fd57_totalLabel_en-US" xlink:label="lab_us-gaap_InterestExpense" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Interest expense, net</link:label>
    <link:label id="lab_us-gaap_InterestExpense_label_en-US" xlink:label="lab_us-gaap_InterestExpense" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Interest Expense, Operating and Nonoperating</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_InterestExpense" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_InterestExpense"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_InterestExpense" xlink:to="lab_us-gaap_InterestExpense" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_IncomeTaxAuthorityAxis_91f73cef-8b81-406f-b01a-2e32d782850b_terseLabel_en-US" xlink:label="lab_us-gaap_IncomeTaxAuthorityAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Income Tax Examination [Line Items]</link:label>
    <link:label id="lab_us-gaap_IncomeTaxAuthorityAxis_label_en-US" xlink:label="lab_us-gaap_IncomeTaxAuthorityAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Income Tax Jurisdiction [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncomeTaxAuthorityAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_IncomeTaxAuthorityAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_IncomeTaxAuthorityAxis" xlink:to="lab_us-gaap_IncomeTaxAuthorityAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_BusinessAcquisitionLineItems_cc6275c5-8b40-43af-baa1-84f616157576_terseLabel_en-US" xlink:label="lab_us-gaap_BusinessAcquisitionLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Business Acquisition [Line Items]</link:label>
    <link:label id="lab_us-gaap_BusinessAcquisitionLineItems_label_en-US" xlink:label="lab_us-gaap_BusinessAcquisitionLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Business Acquisition [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_BusinessAcquisitionLineItems" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_BusinessAcquisitionLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_BusinessAcquisitionLineItems" xlink:to="lab_us-gaap_BusinessAcquisitionLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_EffectiveIncomeTaxRateReconciliationNondeductibleExpenseShareBasedCompensationCost_e92e3b01-098e-46ee-a455-aef85165f750_terseLabel_en-US" xlink:label="lab_us-gaap_EffectiveIncomeTaxRateReconciliationNondeductibleExpenseShareBasedCompensationCost" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Effective Income Tax Rate Reconciliation, Nondeductible Expense, Share-based Payment Arrangement, Percent</link:label>
    <link:label id="lab_us-gaap_EffectiveIncomeTaxRateReconciliationNondeductibleExpenseShareBasedCompensationCost_label_en-US" xlink:label="lab_us-gaap_EffectiveIncomeTaxRateReconciliationNondeductibleExpenseShareBasedCompensationCost" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Effective Income Tax Rate Reconciliation, Nondeductible Expense, Share-Based Payment Arrangement, Percent</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_EffectiveIncomeTaxRateReconciliationNondeductibleExpenseShareBasedCompensationCost" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_EffectiveIncomeTaxRateReconciliationNondeductibleExpenseShareBasedCompensationCost"/>
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    <link:label id="lab_ecd_AllAdjToCompMember_terseLabel_en-US" xlink:label="lab_ecd_AllAdjToCompMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">All Adjustments to Compensation</link:label>
    <link:label id="lab_ecd_AllAdjToCompMember_label_en-US" xlink:label="lab_ecd_AllAdjToCompMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">All Adjustments to Compensation [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_AllAdjToCompMember" xlink:href="https://xbrl.sec.gov/ecd/2024/ecd-2024.xsd#ecd_AllAdjToCompMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_AllAdjToCompMember" xlink:to="lab_ecd_AllAdjToCompMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_EmployeeRelatedLiabilitiesCurrent_b4481f08-53d8-478c-917f-38d24522829d_terseLabel_en-US" xlink:label="lab_us-gaap_EmployeeRelatedLiabilitiesCurrent" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Accrued payroll and fringe benefits</link:label>
    <link:label id="lab_us-gaap_EmployeeRelatedLiabilitiesCurrent_label_en-US" xlink:label="lab_us-gaap_EmployeeRelatedLiabilitiesCurrent" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Employee-related Liabilities, Current</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_EmployeeRelatedLiabilitiesCurrent" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_EmployeeRelatedLiabilitiesCurrent"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_EmployeeRelatedLiabilitiesCurrent" xlink:to="lab_us-gaap_EmployeeRelatedLiabilitiesCurrent" xlink:type="arc" order="1"/>
    <link:label id="lab_codi_InitialTermAndRevolvingLoanCommitment_b676e122-29c7-4081-bf89-db19f2a85ffd_terseLabel_en-US" xlink:label="lab_codi_InitialTermAndRevolvingLoanCommitment" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Initial Term and Revolving Loan Commitment</link:label>
    <link:label id="lab_codi_InitialTermAndRevolvingLoanCommitment_label_en-US" xlink:label="lab_codi_InitialTermAndRevolvingLoanCommitment" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Initial Term and Revolving Loan Commitment</link:label>
    <link:label id="lab_codi_InitialTermAndRevolvingLoanCommitment_documentation_en-US" xlink:label="lab_codi_InitialTermAndRevolvingLoanCommitment" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Initial Term and Revolving Loan Commitment</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_codi_InitialTermAndRevolvingLoanCommitment" xlink:href="codi-20241231.xsd#codi_InitialTermAndRevolvingLoanCommitment"/>
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    <link:label id="lab_us-gaap_IncreaseDecreaseInPrepaidDeferredExpenseAndOtherAssets_b84904bc-462a-4c0d-b5d8-5f6d071cb244_negatedLabel_en-US" xlink:label="lab_us-gaap_IncreaseDecreaseInPrepaidDeferredExpenseAndOtherAssets" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:type="resource" xml:lang="en-US">Other current and non-current assets</link:label>
    <link:label id="lab_us-gaap_IncreaseDecreaseInPrepaidDeferredExpenseAndOtherAssets_label_en-US" xlink:label="lab_us-gaap_IncreaseDecreaseInPrepaidDeferredExpenseAndOtherAssets" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Increase (Decrease) in Prepaid Expense and Other Assets</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncreaseDecreaseInPrepaidDeferredExpenseAndOtherAssets" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_IncreaseDecreaseInPrepaidDeferredExpenseAndOtherAssets"/>
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    <link:label id="lab_us-gaap_MinorityInterestTable_97cdfaa8-89b1-4e99-a564-45d725aac601_terseLabel_en-US" xlink:label="lab_us-gaap_MinorityInterestTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Noncontrolling Interest [Table]</link:label>
    <link:label id="lab_us-gaap_MinorityInterestTable_label_en-US" xlink:label="lab_us-gaap_MinorityInterestTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Noncontrolling Interest [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_MinorityInterestTable" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_MinorityInterestTable"/>
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    <link:label id="lab_us-gaap_TaxCreditCarryforwardAxis_0a35a86e-212e-4447-a3a6-1c13aa2f4e17_terseLabel_en-US" xlink:label="lab_us-gaap_TaxCreditCarryforwardAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Tax Credit Carryforward [Axis]</link:label>
    <link:label id="lab_us-gaap_TaxCreditCarryforwardAxis_label_en-US" xlink:label="lab_us-gaap_TaxCreditCarryforwardAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Tax Credit Carryforward [Axis]</link:label>
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    <link:label id="lab_us-gaap_CommitmentsAndContingenciesDisclosureAbstract_3036f0be-603e-4bc4-a54d-567e9a2536b8_terseLabel_en-US" xlink:label="lab_us-gaap_CommitmentsAndContingenciesDisclosureAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Commitments and Contingencies Disclosure [Abstract]</link:label>
    <link:label id="lab_us-gaap_CommitmentsAndContingenciesDisclosureAbstract_label_en-US" xlink:label="lab_us-gaap_CommitmentsAndContingenciesDisclosureAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Commitments and Contingencies Disclosure [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CommitmentsAndContingenciesDisclosureAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_CommitmentsAndContingenciesDisclosureAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CommitmentsAndContingenciesDisclosureAbstract" xlink:to="lab_us-gaap_CommitmentsAndContingenciesDisclosureAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_LegalEntityAxis_9c836f7b-54f2-4ab4-a60f-dfca0f15d799_terseLabel_en-US" xlink:label="lab_dei_LegalEntityAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Legal Entity [Axis]</link:label>
    <link:label id="lab_dei_LegalEntityAxis_label_en-US" xlink:label="lab_dei_LegalEntityAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Legal Entity [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_LegalEntityAxis" xlink:href="https://xbrl.sec.gov/dei/2024/dei-2024.xsd#dei_LegalEntityAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_LegalEntityAxis" xlink:to="lab_dei_LegalEntityAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_InterestIncomeExpenseNonoperatingNet_3bb4dba1-b9ee-4dff-8a61-1c23c5bf620c_terseLabel_en-US" xlink:label="lab_us-gaap_InterestIncomeExpenseNonoperatingNet" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Interest expense, net</link:label>
    <link:label id="lab_us-gaap_InterestIncomeExpenseNonoperatingNet_label_en-US" xlink:label="lab_us-gaap_InterestIncomeExpenseNonoperatingNet" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Interest Income (Expense), Nonoperating</link:label>
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    <link:label id="lab_us-gaap_SubsegmentsConsolidationItemsDomain_0ae86249-d155-4308-8f98-4678b22b0d50_terseLabel_en-US" xlink:label="lab_us-gaap_SubsegmentsConsolidationItemsDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Subsegments Consolidation Items [Domain]</link:label>
    <link:label id="lab_us-gaap_SubsegmentsConsolidationItemsDomain_label_en-US" xlink:label="lab_us-gaap_SubsegmentsConsolidationItemsDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Subsegments Consolidation Items [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SubsegmentsConsolidationItemsDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_SubsegmentsConsolidationItemsDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_SubsegmentsConsolidationItemsDomain" xlink:to="lab_us-gaap_SubsegmentsConsolidationItemsDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_codi_ArnoldMember_1225f9e0-9a37-4387-820b-9e055010361e_terseLabel_en-US" xlink:label="lab_codi_ArnoldMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Arnold</link:label>
    <link:label id="lab_codi_ArnoldMember_label_en-US" xlink:label="lab_codi_ArnoldMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Arnold [Member]</link:label>
    <link:label id="lab_codi_ArnoldMember_documentation_en-US" xlink:label="lab_codi_ArnoldMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Arnold.</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_codi_ArnoldMember" xlink:href="codi-20241231.xsd#codi_ArnoldMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_codi_ArnoldMember" xlink:to="lab_codi_ArnoldMember" xlink:type="arc" order="1"/>
    <link:label id="lab_srt_ScenarioUnspecifiedDomain_1f68537d-8d04-4649-9270-cad771cbf10c_terseLabel_en-US" xlink:label="lab_srt_ScenarioUnspecifiedDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Scenario [Domain]</link:label>
    <link:label id="lab_srt_ScenarioUnspecifiedDomain_label_en-US" xlink:label="lab_srt_ScenarioUnspecifiedDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Scenario [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_srt_ScenarioUnspecifiedDomain" xlink:href="https://xbrl.fasb.org/srt/2024/elts/srt-2024.xsd#srt_ScenarioUnspecifiedDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_srt_ScenarioUnspecifiedDomain" xlink:to="lab_srt_ScenarioUnspecifiedDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_codi_PercentageOwnershipPrimaryMember_82689d2c-0816-4d6f-b5c8-dc6a63279a6a_terseLabel_en-US" xlink:label="lab_codi_PercentageOwnershipPrimaryMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Primary</link:label>
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    <link:label id="lab_codi_PercentageOwnershipPrimaryMember_documentation_en-US" xlink:label="lab_codi_PercentageOwnershipPrimaryMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Percentage ownership primary.</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_codi_PercentageOwnershipPrimaryMember" xlink:href="codi-20241231.xsd#codi_PercentageOwnershipPrimaryMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_codi_PercentageOwnershipPrimaryMember" xlink:to="lab_codi_PercentageOwnershipPrimaryMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_RelatedPartyTransactionAxis_049e16e6-6a95-454c-8bdd-b87339958c94_terseLabel_en-US" xlink:label="lab_us-gaap_RelatedPartyTransactionAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Related Party Transaction [Axis]</link:label>
    <link:label id="lab_us-gaap_RelatedPartyTransactionAxis_label_en-US" xlink:label="lab_us-gaap_RelatedPartyTransactionAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Related Party Transaction [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_RelatedPartyTransactionAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_RelatedPartyTransactionAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_RelatedPartyTransactionAxis" xlink:to="lab_us-gaap_RelatedPartyTransactionAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_codi_PaymentsOfDistributionsToShareholders_4326f944-fbcf-4004-8e9c-93ae79b6df86_negatedLabel_en-US" xlink:label="lab_codi_PaymentsOfDistributionsToShareholders" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:type="resource" xml:lang="en-US">Distributions paid - common shares</link:label>
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    <link:label id="lab_codi_PaymentsOfDistributionsToShareholders_documentation_en-US" xlink:label="lab_codi_PaymentsOfDistributionsToShareholders" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Payments of distributions to shareholders.</link:label>
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    <link:label id="lab_codi_ArnoldMagneticsMember_af7e27d5-5754-46af-8c29-7282dda046eb_terseLabel_en-US" xlink:label="lab_codi_ArnoldMagneticsMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Arnold Magnetics</link:label>
    <link:label id="lab_codi_ArnoldMagneticsMember_2a1f36e5-34af-468b-9f7f-e584b54549b9_verboseLabel_en-US" xlink:label="lab_codi_ArnoldMagneticsMember" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Arnold Magnetics [Member]</link:label>
    <link:label id="lab_codi_ArnoldMagneticsMember_label_en-US" xlink:label="lab_codi_ArnoldMagneticsMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Arnold Magnetics [Member]</link:label>
    <link:label id="lab_codi_ArnoldMagneticsMember_documentation_en-US" xlink:label="lab_codi_ArnoldMagneticsMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Arnold magnetics.</link:label>
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    <link:label id="lab_us-gaap_LongtermDebtTypeDomain_9a0fad07-928f-42bd-861b-e151e6ef8f75_terseLabel_en-US" xlink:label="lab_us-gaap_LongtermDebtTypeDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Long-term Debt, Type [Domain]</link:label>
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    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LongtermDebtTypeDomain" xlink:to="lab_us-gaap_LongtermDebtTypeDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_EntityAddressStateOrProvince_465bd53d-8abb-4b6e-a94f-8a0f4d67d735_terseLabel_en-US" xlink:label="lab_dei_EntityAddressStateOrProvince" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Entity Address, State or Province</link:label>
    <link:label id="lab_dei_EntityAddressStateOrProvince_label_en-US" xlink:label="lab_dei_EntityAddressStateOrProvince" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Entity Address, State or Province</link:label>
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    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_EntityAddressStateOrProvince" xlink:to="lab_dei_EntityAddressStateOrProvince" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_ErrCompAnalysisTextBlock_terseLabel_en-US" xlink:label="lab_ecd_ErrCompAnalysisTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Erroneous Compensation Analysis</link:label>
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    <link:label id="lab_us-gaap_AssetsOfDisposalGroupIncludingDiscontinuedOperationCurrent_bbf1c252-e358-44c9-a621-b16b059bdae5_terseLabel_en-US" xlink:label="lab_us-gaap_AssetsOfDisposalGroupIncludingDiscontinuedOperationCurrent" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Current assets of discontinued operations</link:label>
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    <link:label id="lab_us-gaap_TransfersAndServicingOfFinancialInstrumentsTypesOfFinancialInstrumentsDomain_6b3b3b72-43f3-47e5-90ed-00d125f503a6_terseLabel_en-US" xlink:label="lab_us-gaap_TransfersAndServicingOfFinancialInstrumentsTypesOfFinancialInstrumentsDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Financial Instruments [Domain]</link:label>
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    <link:label id="lab_us-gaap_DeferredChargesPolicyTextBlock_9b3ec776-4bb3-48dc-b816-cb2368e32b5c_terseLabel_en-US" xlink:label="lab_us-gaap_DeferredChargesPolicyTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Deferred Debt Issuance Costs</link:label>
    <link:label id="lab_us-gaap_DeferredChargesPolicyTextBlock_label_en-US" xlink:label="lab_us-gaap_DeferredChargesPolicyTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Deferred Charges, Policy [Policy Text Block]</link:label>
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    <link:label id="lab_us-gaap_LiabilitiesAndStockholdersEquityAbstract_aedc5763-e5a1-43cd-a92e-5d7cb6c40299_terseLabel_en-US" xlink:label="lab_us-gaap_LiabilitiesAndStockholdersEquityAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Liabilities and stockholders&#8217; equity</link:label>
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    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DebtInstrumentPeriodicPayment" xlink:to="lab_us-gaap_DebtInstrumentPeriodicPayment" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DisposalGroupIncludingDiscontinuedOperationOtherCurrentLiabilities_d50d3eaf-6d02-4d3a-912e-d312da27bdab_terseLabel_en-US" xlink:label="lab_us-gaap_DisposalGroupIncludingDiscontinuedOperationOtherCurrentLiabilities" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Disposal Group, Including Discontinued Operation, Other Liabilities, Current</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DisposalGroupIncludingDiscontinuedOperationOtherCurrentLiabilities" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_DisposalGroupIncludingDiscontinuedOperationOtherCurrentLiabilities"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DisposalGroupIncludingDiscontinuedOperationOtherCurrentLiabilities" xlink:to="lab_us-gaap_DisposalGroupIncludingDiscontinuedOperationOtherCurrentLiabilities" xlink:type="arc" order="1"/>
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    <link:loc xlink:type="locator" xlink:label="loc_ecd_PvpTable" xlink:href="https://xbrl.sec.gov/ecd/2024/ecd-2024.xsd#ecd_PvpTable"/>
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    <link:label id="lab_us-gaap_ScheduleOfPropertyPlantAndEquipmentTable_2b3edae7-97d5-40ed-86ff-6529b9801ef6_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfPropertyPlantAndEquipmentTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Property, Plant and Equipment [Table]</link:label>
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    <link:label id="lab_us-gaap_DisposalGroupIncludingDiscontinuedOperationAccruedLiabilitiesCurrent_bb487805-2e0a-431d-a708-f460f13984fd_terseLabel_en-US" xlink:label="lab_us-gaap_DisposalGroupIncludingDiscontinuedOperationAccruedLiabilitiesCurrent" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Disposal Group, Including Discontinued Operation, Accrued Liabilities, Current</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DefinedBenefitPlanPlanAmendments" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_DefinedBenefitPlanPlanAmendments"/>
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    <link:label id="lab_us-gaap_AdditionalFinancialInformationDisclosureTextBlock_e82b0684-edee-4b4c-8d29-ded462dc8ca7_terseLabel_en-US" xlink:label="lab_us-gaap_AdditionalFinancialInformationDisclosureTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Supplemental Data</link:label>
    <link:label id="lab_us-gaap_AdditionalFinancialInformationDisclosureTextBlock_label_en-US" xlink:label="lab_us-gaap_AdditionalFinancialInformationDisclosureTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Additional Financial Information Disclosure [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AdditionalFinancialInformationDisclosureTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_AdditionalFinancialInformationDisclosureTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AdditionalFinancialInformationDisclosureTextBlock" xlink:to="lab_us-gaap_AdditionalFinancialInformationDisclosureTextBlock" xlink:type="arc" order="1"/>
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    <link:label id="lab_codi_PrimaLoftMember_documentation_en-US" xlink:label="lab_codi_PrimaLoftMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">PrimaLoft</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_codi_PrimaLoftMember" xlink:href="codi-20241231.xsd#codi_PrimaLoftMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_codi_PrimaLoftMember" xlink:to="lab_codi_PrimaLoftMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_SubsequentEventMember_ddc78a2d-d879-4092-8c20-b5a7741fdbda_terseLabel_en-US" xlink:label="lab_us-gaap_SubsequentEventMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Subsequent Event [Member]</link:label>
    <link:label id="lab_us-gaap_SubsequentEventMember_label_en-US" xlink:label="lab_us-gaap_SubsequentEventMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Subsequent Event [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SubsequentEventMember" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_SubsequentEventMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_SubsequentEventMember" xlink:to="lab_us-gaap_SubsequentEventMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_StockIssuedDuringPeriodValueStockOptionsExercised_b087ee1b-e633-4c50-86a6-b074a7c43d1a_terseLabel_en-US" xlink:label="lab_us-gaap_StockIssuedDuringPeriodValueStockOptionsExercised" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Effect of subsidiary stock option exercise</link:label>
    <link:label id="lab_us-gaap_StockIssuedDuringPeriodValueStockOptionsExercised_label_en-US" xlink:label="lab_us-gaap_StockIssuedDuringPeriodValueStockOptionsExercised" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Stock Issued During Period, Value, Stock Options Exercised</link:label>
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    <link:label id="lab_us-gaap_SubsegmentsDomain_2d2d00bf-c199-4f7d-927b-362d07316bf0_terseLabel_en-US" xlink:label="lab_us-gaap_SubsegmentsDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Subsegments [Domain]</link:label>
    <link:label id="lab_us-gaap_SubsegmentsDomain_label_en-US" xlink:label="lab_us-gaap_SubsegmentsDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Subsegments [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SubsegmentsDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_SubsegmentsDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_SubsegmentsDomain" xlink:to="lab_us-gaap_SubsegmentsDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_IncomeTaxPolicyTextBlock_fa4496a3-546d-45a0-92e8-6c3ac9947d0b_terseLabel_en-US" xlink:label="lab_us-gaap_IncomeTaxPolicyTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Deferred Income Taxes</link:label>
    <link:label id="lab_us-gaap_IncomeTaxPolicyTextBlock_label_en-US" xlink:label="lab_us-gaap_IncomeTaxPolicyTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Income Tax, Policy [Policy Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncomeTaxPolicyTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_IncomeTaxPolicyTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_IncomeTaxPolicyTextBlock" xlink:to="lab_us-gaap_IncomeTaxPolicyTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_PeerGroupIssuersFnTextBlock_terseLabel_en-US" xlink:label="lab_ecd_PeerGroupIssuersFnTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Peer Group Issuers, Footnote</link:label>
    <link:label id="lab_ecd_PeerGroupIssuersFnTextBlock_label_en-US" xlink:label="lab_ecd_PeerGroupIssuersFnTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Peer Group Issuers, Footnote [Text Block]</link:label>
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    <link:label id="lab_us-gaap_SegmentDomain_b2a55c53-9dd6-4b49-9998-4c66faf11c2c_terseLabel_en-US" xlink:label="lab_us-gaap_SegmentDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Segments [Domain]</link:label>
    <link:label id="lab_us-gaap_SegmentDomain_label_en-US" xlink:label="lab_us-gaap_SegmentDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Segments [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SegmentDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_SegmentDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_SegmentDomain" xlink:to="lab_us-gaap_SegmentDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ReconciliationOfUnrecognizedTaxBenefitsExcludingAmountsPertainingToExaminedTaxReturnsRollForward_781d227e-ca4d-4896-9e74-b296aca87974_terseLabel_en-US" xlink:label="lab_us-gaap_ReconciliationOfUnrecognizedTaxBenefitsExcludingAmountsPertainingToExaminedTaxReturnsRollForward" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Unrecognized Tax Benefits [Roll Forward]</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ReconciliationOfUnrecognizedTaxBenefitsExcludingAmountsPertainingToExaminedTaxReturnsRollForward" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_ReconciliationOfUnrecognizedTaxBenefitsExcludingAmountsPertainingToExaminedTaxReturnsRollForward"/>
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    <link:label id="lab_codi_TermLoanMember_3b604bf6-0de0-46d3-9da5-ef34bb17d569_terseLabel_en-US" xlink:label="lab_codi_TermLoanMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Term Loan</link:label>
    <link:label id="lab_codi_TermLoanMember_label_en-US" xlink:label="lab_codi_TermLoanMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Term Loan [Member]</link:label>
    <link:label id="lab_codi_TermLoanMember_documentation_en-US" xlink:label="lab_codi_TermLoanMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Term Loan [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_codi_TermLoanMember" xlink:href="codi-20241231.xsd#codi_TermLoanMember"/>
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    <link:label id="lab_us-gaap_IncomeLossFromDiscontinuedOperationsNetOfTaxPerDilutedShare_6cf91b19-e642-468a-afd8-70045332bdda_terseLabel_en-US" xlink:label="lab_us-gaap_IncomeLossFromDiscontinuedOperationsNetOfTaxPerDilutedShare" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Income (Loss) from Discontinued Operations and Disposal of Discontinued Operations, Net of Tax, Per Diluted Share</link:label>
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    <link:label id="lab_ecd_PeoMember_terseLabel_en-US" xlink:label="lab_ecd_PeoMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">PEO</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_ecd_PeoMember" xlink:href="https://xbrl.sec.gov/ecd/2024/ecd-2024.xsd#ecd_PeoMember"/>
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    <link:label id="lab_us-gaap_DeferredTaxAssetDomain_d553e9dc-080f-4cfa-a5e4-04272ff5524e_terseLabel_en-US" xlink:label="lab_us-gaap_DeferredTaxAssetDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Deferred Tax Asset [Domain]</link:label>
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    <link:label id="lab_us-gaap_DefinedBenefitPlanFundedStatusOfPlan_2bd90240-2054-418f-9170-17cabb3a449a_verboseLabel_en-US" xlink:label="lab_us-gaap_DefinedBenefitPlanFundedStatusOfPlan" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Unfunded liability</link:label>
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    <link:label id="lab_us-gaap_PropertyPlantAndEquipmentByTypeAxis_7495f4db-1cb5-47b7-8932-63d28683f4e0_terseLabel_en-US" xlink:label="lab_us-gaap_PropertyPlantAndEquipmentByTypeAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Property, Plant and Equipment, Type [Axis]</link:label>
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    <link:label id="lab_dei_EntityPublicFloat_label_en-US" xlink:label="lab_dei_EntityPublicFloat" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Entity Public Float</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityPublicFloat" xlink:href="https://xbrl.sec.gov/dei/2024/dei-2024.xsd#dei_EntityPublicFloat"/>
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    <link:label id="lab_us-gaap_IncomeLossFromEquityMethodInvestments_ca47aaeb-5785-4f54-a5ed-1956dd15a451_terseLabel_en-US" xlink:label="lab_us-gaap_IncomeLossFromEquityMethodInvestments" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Income (Loss) from Equity Method Investments</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncomeLossFromEquityMethodInvestments" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_IncomeLossFromEquityMethodInvestments"/>
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    <link:label id="lab_us-gaap_TreasuryStockCommonValue_label_en-US" xlink:label="lab_us-gaap_TreasuryStockCommonValue" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Treasury Stock, Common, Value</link:label>
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    <link:label id="lab_us-gaap_DefinedBenefitPlanBenefitObligation_d5db26c0-1792-48bd-bf33-4aada334cf82_periodStartLabel_en-US" xlink:label="lab_us-gaap_DefinedBenefitPlanBenefitObligation" xlink:role="http://www.xbrl.org/2003/role/periodStartLabel" xlink:type="resource" xml:lang="en-US">Benefit obligation, beginning of year</link:label>
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    <link:label id="lab_us-gaap_DefinedBenefitPlanBenefitObligation_f24bf086-df25-4fa2-8426-d6d2ea88347a_terseLabel_en-US" xlink:label="lab_us-gaap_DefinedBenefitPlanBenefitObligation" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Defined Benefit Plan, Benefit Obligation</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DefinedBenefitPlanBenefitObligation" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_DefinedBenefitPlanBenefitObligation"/>
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    <link:label id="lab_us-gaap_IncomeLossFromContinuingOperationsBeforeIncomeTaxesMinorityInterestAndIncomeLossFromEquityMethodInvestments_0419de5d-0e37-4bd6-85f6-a4e5d03044a0_verboseLabel_en-US" xlink:label="lab_us-gaap_IncomeLossFromContinuingOperationsBeforeIncomeTaxesMinorityInterestAndIncomeLossFromEquityMethodInvestments" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Loss from continuing operations before income taxes</link:label>
    <link:label id="lab_us-gaap_IncomeLossFromContinuingOperationsBeforeIncomeTaxesMinorityInterestAndIncomeLossFromEquityMethodInvestments_label_en-US" xlink:label="lab_us-gaap_IncomeLossFromContinuingOperationsBeforeIncomeTaxesMinorityInterestAndIncomeLossFromEquityMethodInvestments" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Income (Loss) from Continuing Operations before Equity Method Investments, Income Taxes, Noncontrolling Interest</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncomeLossFromContinuingOperationsBeforeIncomeTaxesMinorityInterestAndIncomeLossFromEquityMethodInvestments" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_IncomeLossFromContinuingOperationsBeforeIncomeTaxesMinorityInterestAndIncomeLossFromEquityMethodInvestments"/>
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    <link:label id="lab_codi_MarucciAndACIMember_93341906-3aee-40b5-8e5d-ebde1a277002_terseLabel_en-US" xlink:label="lab_codi_MarucciAndACIMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Marucci and ACI</link:label>
    <link:label id="lab_codi_MarucciAndACIMember_label_en-US" xlink:label="lab_codi_MarucciAndACIMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Marucci and ACI [Member]</link:label>
    <link:label id="lab_codi_MarucciAndACIMember_documentation_en-US" xlink:label="lab_codi_MarucciAndACIMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Marucci and ACI</link:label>
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    <link:label id="lab_ecd_AwardsCloseToMnpiDiscTableTextBlock_terseLabel_en-US" xlink:label="lab_ecd_AwardsCloseToMnpiDiscTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Awards Close in Time to MNPI Disclosures, Table</link:label>
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    <link:label id="lab_codi_LifoamMember_b576b2f8-0c57-4108-8e13-53f7a3fd0032_terseLabel_en-US" xlink:label="lab_codi_LifoamMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Lifoam</link:label>
    <link:label id="lab_codi_LifoamMember_label_en-US" xlink:label="lab_codi_LifoamMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Lifoam [Member]</link:label>
    <link:label id="lab_codi_LifoamMember_documentation_en-US" xlink:label="lab_codi_LifoamMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Lifoam</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_codi_LifoamMember" xlink:href="codi-20241231.xsd#codi_LifoamMember"/>
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    <link:label id="lab_srt_ValuationAndQualifyingAccountsAbstract_e88abd80-5aa0-46aa-bd00-629817576c66_terseLabel_en-US" xlink:label="lab_srt_ValuationAndQualifyingAccountsAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">SEC Schedule, 12-09, Valuation and Qualifying Accounts [Abstract]</link:label>
    <link:label id="lab_srt_ValuationAndQualifyingAccountsAbstract_label_en-US" xlink:label="lab_srt_ValuationAndQualifyingAccountsAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">SEC Schedule, 12-09, Valuation and Qualifying Accounts [Abstract]</link:label>
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    <link:label id="lab_ecd_FrValAsOfPrrYrEndOfEqtyAwrdsGrntdInPrrYrsFldVstngCondsDrngCvrdYrMember_terseLabel_en-US" xlink:label="lab_ecd_FrValAsOfPrrYrEndOfEqtyAwrdsGrntdInPrrYrsFldVstngCondsDrngCvrdYrMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Prior Year End Fair Value of Equity Awards Granted in Any Prior Year that Fail to Meet Applicable Vesting Conditions During Covered Year</link:label>
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    <link:label id="lab_us-gaap_RetirementPlanSponsorLocationDomain_8fd862cb-cf66-4f2d-8cb6-984535f5dc27_terseLabel_en-US" xlink:label="lab_us-gaap_RetirementPlanSponsorLocationDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Retirement Plan Sponsor Location [Domain]</link:label>
    <link:label id="lab_us-gaap_RetirementPlanSponsorLocationDomain_label_en-US" xlink:label="lab_us-gaap_RetirementPlanSponsorLocationDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Retirement Plan Sponsor Location [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_RetirementPlanSponsorLocationDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_RetirementPlanSponsorLocationDomain"/>
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    <link:label id="lab_us-gaap_DeferredRevenue_91c7b61f-0b0e-4c0b-9c23-728135b13ec5_terseLabel_en-US" xlink:label="lab_us-gaap_DeferredRevenue" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Deferred Revenue</link:label>
    <link:label id="lab_us-gaap_DeferredRevenue_label_en-US" xlink:label="lab_us-gaap_DeferredRevenue" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Deferred Revenue</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DeferredRevenue" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_DeferredRevenue"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DeferredRevenue" xlink:to="lab_us-gaap_DeferredRevenue" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_AggtErrCompAmt_terseLabel_en-US" xlink:label="lab_ecd_AggtErrCompAmt" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Aggregate Erroneous Compensation Amount</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_ecd_AggtErrCompAmt" xlink:href="https://xbrl.sec.gov/ecd/2024/ecd-2024.xsd#ecd_AggtErrCompAmt"/>
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    <link:label id="lab_us-gaap_DisposalGroupIncludingDiscontinuedOperationGrossProfitLoss_7c9ff102-a90c-48ca-a4a3-60587fadbcc4_terseLabel_en-US" xlink:label="lab_us-gaap_DisposalGroupIncludingDiscontinuedOperationGrossProfitLoss" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Gross profit</link:label>
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    <link:label id="lab_dei_LocalPhoneNumber_438d16e6-ecf1-4cf9-9fac-b23e48c15ab3_terseLabel_en-US" xlink:label="lab_dei_LocalPhoneNumber" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Local Phone Number</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_dei_LocalPhoneNumber" xlink:href="https://xbrl.sec.gov/dei/2024/dei-2024.xsd#dei_LocalPhoneNumber"/>
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    <link:label id="lab_us-gaap_IntangibleAssetsGrossExcludingGoodwill_a8c64e89-9269-4a58-af81-311dd7662059_totalLabel_en-US" xlink:label="lab_us-gaap_IntangibleAssetsGrossExcludingGoodwill" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Intangible Assets, Gross (Excluding Goodwill)</link:label>
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    <link:label id="lab_us-gaap_IntangibleAssetsGrossExcludingGoodwill_label_en-US" xlink:label="lab_us-gaap_IntangibleAssetsGrossExcludingGoodwill" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Intangible Assets, Gross (Excluding Goodwill)</link:label>
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    <link:label id="lab_us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedLiabilitiesAbstract_d504026b-6e3b-4327-b154-a119d8d6b30e_terseLabel_en-US" xlink:label="lab_us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedLiabilitiesAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Liabilities and noncontrolling interest:</link:label>
    <link:label id="lab_us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedLiabilitiesAbstract_label_en-US" xlink:label="lab_us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedLiabilitiesAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Business Combination, Recognized Identifiable Assets Acquired and Liabilities Assumed, Liabilities [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedLiabilitiesAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedLiabilitiesAbstract"/>
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    <link:label id="lab_us-gaap_DeferredTaxAssetsValuationAllowance_8483c7bf-b1fd-4f77-887f-fcd1b22ee53a_terseLabel_en-US" xlink:label="lab_us-gaap_DeferredTaxAssetsValuationAllowance" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Valuation allowance</link:label>
    <link:label id="lab_us-gaap_DeferredTaxAssetsValuationAllowance_367d03b6-779e-4124-8ea2-ce54ee00baae_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_DeferredTaxAssetsValuationAllowance" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Valuation allowance</link:label>
    <link:label id="lab_us-gaap_DeferredTaxAssetsValuationAllowance_e1033f03-c020-498d-9503-8454d575f3e7_negatedLabel_en-US" xlink:label="lab_us-gaap_DeferredTaxAssetsValuationAllowance" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:type="resource" xml:lang="en-US">Valuation allowance</link:label>
    <link:label id="lab_us-gaap_DeferredTaxAssetsValuationAllowance_label_en-US" xlink:label="lab_us-gaap_DeferredTaxAssetsValuationAllowance" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Deferred Tax Assets, Valuation Allowance</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DeferredTaxAssetsValuationAllowance" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_DeferredTaxAssetsValuationAllowance"/>
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    <link:label id="lab_ecd_AggtErrCompNotYetDeterminedTextBlock_terseLabel_en-US" xlink:label="lab_ecd_AggtErrCompNotYetDeterminedTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Aggregate Erroneous Compensation Not Yet Determined</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_ecd_AggtErrCompNotYetDeterminedTextBlock" xlink:href="https://xbrl.sec.gov/ecd/2024/ecd-2024.xsd#ecd_AggtErrCompNotYetDeterminedTextBlock"/>
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    <link:label id="lab_codi_OtherInternationalMember_8aa2449c-bcaa-41b5-aeb8-6a595bd6a91b_terseLabel_en-US" xlink:label="lab_codi_OtherInternationalMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Other International [Member]</link:label>
    <link:label id="lab_codi_OtherInternationalMember_label_en-US" xlink:label="lab_codi_OtherInternationalMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Other International [Member]</link:label>
    <link:label id="lab_codi_OtherInternationalMember_documentation_en-US" xlink:label="lab_codi_OtherInternationalMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Other International [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_codi_OtherInternationalMember" xlink:href="codi-20241231.xsd#codi_OtherInternationalMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_codi_OtherInternationalMember" xlink:to="lab_codi_OtherInternationalMember" xlink:type="arc" order="1"/>
    <link:label id="lab_codi_DeferredTaxAssetLeases_64221dba-1718-49df-a0ef-e6e8288ecfca_terseLabel_en-US" xlink:label="lab_codi_DeferredTaxAssetLeases" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Deferred Tax Asset, Leases</link:label>
    <link:label id="lab_codi_DeferredTaxAssetLeases_label_en-US" xlink:label="lab_codi_DeferredTaxAssetLeases" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Deferred Tax Asset, Leases</link:label>
    <link:label id="lab_codi_DeferredTaxAssetLeases_documentation_en-US" xlink:label="lab_codi_DeferredTaxAssetLeases" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Deferred Tax Asset, Leases</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_codi_DeferredTaxAssetLeases" xlink:href="codi-20241231.xsd#codi_DeferredTaxAssetLeases"/>
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    <link:label id="lab_us-gaap_PostemploymentBenefitsAbstract_95bd6e7e-099b-4e54-bbf2-c2976be99a13_terseLabel_en-US" xlink:label="lab_us-gaap_PostemploymentBenefitsAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Postemployment Benefits [Abstract]</link:label>
    <link:label id="lab_us-gaap_PostemploymentBenefitsAbstract_label_en-US" xlink:label="lab_us-gaap_PostemploymentBenefitsAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Postemployment Benefits [Abstract]</link:label>
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    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PostemploymentBenefitsAbstract" xlink:to="lab_us-gaap_PostemploymentBenefitsAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_codi_NumberOfBusinessesOwned_2c5a6042-aa4e-4ed8-8750-4321bc7970c9_terseLabel_en-US" xlink:label="lab_codi_NumberOfBusinessesOwned" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Number of businesses/operating segments owned</link:label>
    <link:label id="lab_codi_NumberOfBusinessesOwned_label_en-US" xlink:label="lab_codi_NumberOfBusinessesOwned" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Number Of Businesses Owned</link:label>
    <link:label id="lab_codi_NumberOfBusinessesOwned_documentation_en-US" xlink:label="lab_codi_NumberOfBusinessesOwned" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Number of businesses owned.</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_codi_NumberOfBusinessesOwned" xlink:href="codi-20241231.xsd#codi_NumberOfBusinessesOwned"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_codi_NumberOfBusinessesOwned" xlink:to="lab_codi_NumberOfBusinessesOwned" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_IncreaseDecreaseInOperatingCapitalAbstract_b06239fc-8ec7-45ec-9405-64457eb6cdb0_terseLabel_en-US" xlink:label="lab_us-gaap_IncreaseDecreaseInOperatingCapitalAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Changes in operating assets and liabilities, net of acquisitions:</link:label>
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    <link:label id="lab_ecd_PeoTotalCompAmt_terseLabel_en-US" xlink:label="lab_ecd_PeoTotalCompAmt" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">PEO Total Compensation Amount</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_ecd_PeoTotalCompAmt" xlink:href="https://xbrl.sec.gov/ecd/2024/ecd-2024.xsd#ecd_PeoTotalCompAmt"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_PeoTotalCompAmt" xlink:to="lab_ecd_PeoTotalCompAmt" xlink:type="arc" order="1"/>
    <link:label id="lab_codi_AllocationInterestsMember_52631db9-ddfc-4fab-a839-fa38a256de78_terseLabel_en-US" xlink:label="lab_codi_AllocationInterestsMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Allocation Interests [Member]</link:label>
    <link:label id="lab_codi_AllocationInterestsMember_label_en-US" xlink:label="lab_codi_AllocationInterestsMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Allocation Interests [Member]</link:label>
    <link:label id="lab_codi_AllocationInterestsMember_documentation_en-US" xlink:label="lab_codi_AllocationInterestsMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Allocation interests.</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_codi_AllocationInterestsMember" xlink:href="codi-20241231.xsd#codi_AllocationInterestsMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_codi_AllocationInterestsMember" xlink:to="lab_codi_AllocationInterestsMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_SeniorNotes_2a64d78d-27e4-4632-9f0c-bd9419c3652d_terseLabel_en-US" xlink:label="lab_us-gaap_SeniorNotes" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Senior notes</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SeniorNotes" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_SeniorNotes"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_SeniorNotes" xlink:to="lab_us-gaap_SeniorNotes" xlink:type="arc" order="1"/>
    <link:label id="lab_codi_DisposalGrouprepaymentofintercompanyloans_8ce148a5-65da-455a-a6e9-8391a4ecc713_terseLabel_en-US" xlink:label="lab_codi_DisposalGrouprepaymentofintercompanyloans" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Disposal Group, repayment of intercompany loans</link:label>
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    <link:label id="lab_codi_AccruedInventory_0b00ba7c-fbb2-4923-b813-8b37c1a50b0c_terseLabel_en-US" xlink:label="lab_codi_AccruedInventory" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Accrued inventory</link:label>
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    <link:label id="lab_us-gaap_PropertyPlantAndEquipmentTypeDomain_54df6038-b382-415f-8aaa-80a847d39776_terseLabel_en-US" xlink:label="lab_us-gaap_PropertyPlantAndEquipmentTypeDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Property, Plant and Equipment, Type [Domain]</link:label>
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    <link:label id="lab_us-gaap_InterestPayableCurrent_label_en-US" xlink:label="lab_us-gaap_InterestPayableCurrent" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Interest Payable, Current</link:label>
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    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_InterestPayableCurrent" xlink:to="lab_us-gaap_InterestPayableCurrent" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_IncomeStatementLocationAxis_dd25307a-ddac-4ec2-a5c4-acd8d8449c4d_terseLabel_en-US" xlink:label="lab_us-gaap_IncomeStatementLocationAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Statement of Income Location, Balance [Axis]</link:label>
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    <link:label id="lab_us-gaap_DefinedBenefitPlanByPlanAssetCategoriesAxis_1dfb3508-0002-4a87-8975-f8c5324b4288_terseLabel_en-US" xlink:label="lab_us-gaap_DefinedBenefitPlanByPlanAssetCategoriesAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Defined Benefit Plan, Plan Assets, Category [Axis]</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DefinedBenefitPlanByPlanAssetCategoriesAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_DefinedBenefitPlanByPlanAssetCategoriesAxis"/>
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    <link:label id="lab_us-gaap_DebtDisclosureAbstract_fe5de936-71a0-41c0-94fe-b4021ce8c1f0_terseLabel_en-US" xlink:label="lab_us-gaap_DebtDisclosureAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Debt Disclosure [Abstract]</link:label>
    <link:label id="lab_us-gaap_DebtDisclosureAbstract_label_en-US" xlink:label="lab_us-gaap_DebtDisclosureAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Disclosure [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtDisclosureAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_DebtDisclosureAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DebtDisclosureAbstract" xlink:to="lab_us-gaap_DebtDisclosureAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CommonStockMember_c1792e47-5799-49e0-9572-0384ea510099_terseLabel_en-US" xlink:label="lab_us-gaap_CommonStockMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Trust Common Shares</link:label>
    <link:label id="lab_us-gaap_CommonStockMember_label_en-US" xlink:label="lab_us-gaap_CommonStockMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Common Stock [Member]</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_ecd_ForgoneRecoveryDueToExpenseOfEnforcementAmt" xlink:href="https://xbrl.sec.gov/ecd/2024/ecd-2024.xsd#ecd_ForgoneRecoveryDueToExpenseOfEnforcementAmt"/>
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    <link:label id="lab_us-gaap_ScheduleOfBusinessAcquisitionsByAcquisitionTable_d6d74aa8-e0b7-4972-a913-6634fe0ea029_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfBusinessAcquisitionsByAcquisitionTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Business Acquisitions, by Acquisition [Table]</link:label>
    <link:label id="lab_us-gaap_ScheduleOfBusinessAcquisitionsByAcquisitionTable_label_en-US" xlink:label="lab_us-gaap_ScheduleOfBusinessAcquisitionsByAcquisitionTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Schedule of Business Acquisitions, by Acquisition [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfBusinessAcquisitionsByAcquisitionTable" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_ScheduleOfBusinessAcquisitionsByAcquisitionTable"/>
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    <link:label id="lab_us-gaap_LineOfCreditMember_02aa3f32-f2c2-4fd6-bd04-63e4324f54f0_terseLabel_en-US" xlink:label="lab_us-gaap_LineOfCreditMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Line of Credit</link:label>
    <link:label id="lab_us-gaap_LineOfCreditMember_label_en-US" xlink:label="lab_us-gaap_LineOfCreditMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Line of Credit [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LineOfCreditMember" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_LineOfCreditMember"/>
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    <link:label id="lab_codi_SeriesCPreferredSharesRepresentingSeriesCTrustPreferredInterestInCompassDiversifiedHoldingsMemberDomain_096d953d-f7cc-49e5-8b15-e4221f492b5e_terseLabel_en-US" xlink:label="lab_codi_SeriesCPreferredSharesRepresentingSeriesCTrustPreferredInterestInCompassDiversifiedHoldingsMemberDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Series C Preferred Shares Representing Series C Trust Preferred Interest In Compass Diversified Holdings [Member] [Domain]</link:label>
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    <link:label id="lab_us-gaap_SegmentReportingAbstract_8e5df8e6-df33-44bb-a72c-abdd2196f231_terseLabel_en-US" xlink:label="lab_us-gaap_SegmentReportingAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Segment Reporting [Abstract]</link:label>
    <link:label id="lab_us-gaap_SegmentReportingAbstract_label_en-US" xlink:label="lab_us-gaap_SegmentReportingAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Segment Reporting [Abstract]</link:label>
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    <link:label id="lab_dei_EntityCentralIndexKey_d929b859-a12c-44ee-811e-027a3194d3fd_terseLabel_en-US" xlink:label="lab_dei_EntityCentralIndexKey" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Entity Central Index Key</link:label>
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    <link:label id="lab_srt_StatementScenarioAxis_c2d8c6bf-7377-4b6e-a4d5-ce6a0698e22f_terseLabel_en-US" xlink:label="lab_srt_StatementScenarioAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Scenario [Axis]</link:label>
    <link:label id="lab_srt_StatementScenarioAxis_label_en-US" xlink:label="lab_srt_StatementScenarioAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Scenario [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_srt_StatementScenarioAxis" xlink:href="https://xbrl.fasb.org/srt/2024/elts/srt-2024.xsd#srt_StatementScenarioAxis"/>
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    <link:label id="lab_codi_A2029SeniorNotesMember_8a86efa9-0a33-4851-b77c-b37f2c16f257_terseLabel_en-US" xlink:label="lab_codi_A2029SeniorNotesMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">2029 Senior Notes</link:label>
    <link:label id="lab_codi_A2029SeniorNotesMember_label_en-US" xlink:label="lab_codi_A2029SeniorNotesMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">2029 Senior Notes [Member]</link:label>
    <link:label id="lab_codi_A2029SeniorNotesMember_documentation_en-US" xlink:label="lab_codi_A2029SeniorNotesMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">2029 Senior Notes</link:label>
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    <link:label id="lab_codi_BusinessCombinationProvisionalInformationInitialAccountingIncompleteAdjustmentOtherLiabilities_e1feed4b-93dd-4ecd-8d67-421a5171e82e_terseLabel_en-US" xlink:label="lab_codi_BusinessCombinationProvisionalInformationInitialAccountingIncompleteAdjustmentOtherLiabilities" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Business Combination, Provisional Information, Initial Accounting Incomplete, Adjustment, Other Liabilities</link:label>
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    <link:label id="lab_us-gaap_DiscontinuedOperationsAndDisposalGroupsAbstract_label_en-US" xlink:label="lab_us-gaap_DiscontinuedOperationsAndDisposalGroupsAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Discontinued Operations and Disposal Groups [Abstract]</link:label>
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    <link:label id="lab_us-gaap_DebtInstrumentUnusedBorrowingCapacityFee_0c17d420-3025-448c-9cf2-1e2af84cb949_terseLabel_en-US" xlink:label="lab_us-gaap_DebtInstrumentUnusedBorrowingCapacityFee" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Unused fee on Revolving Credit Facility</link:label>
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    <link:label id="lab_us-gaap_CorporateMember_20857202-5fd3-4fe6-8b9f-5e0bdb56000f_terseLabel_en-US" xlink:label="lab_us-gaap_CorporateMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Corporate</link:label>
    <link:label id="lab_us-gaap_CorporateMember_label_en-US" xlink:label="lab_us-gaap_CorporateMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Corporate Segment [Member]</link:label>
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    <link:label id="lab_codi_BusinessCombinationStepAcquisitionPPERemeasurement_98786dbd-bf79-4749-80d5-55ee4ab9f850_terseLabel_en-US" xlink:label="lab_codi_BusinessCombinationStepAcquisitionPPERemeasurement" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Business Combination, Step Acquisition, PP&amp;E, Remeasurement</link:label>
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    <link:label id="lab_us-gaap_StockholdersEquityNoteDisclosureTextBlock_f3f23b35-ed7a-4138-a526-17a42f2f8b5a_terseLabel_en-US" xlink:label="lab_us-gaap_StockholdersEquityNoteDisclosureTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Stockholder's Equity</link:label>
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    <link:label id="lab_us-gaap_LongTermDebtCurrent_d4a5b9df-f93c-4721-8b6d-e07eb4b81647_negatedLabel_en-US" xlink:label="lab_us-gaap_LongTermDebtCurrent" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:type="resource" xml:lang="en-US">Less: Current portion, term loan facilities</link:label>
    <link:label id="lab_us-gaap_LongTermDebtCurrent_label_en-US" xlink:label="lab_us-gaap_LongTermDebtCurrent" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Long-Term Debt, Current Maturities</link:label>
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    <link:label id="lab_us-gaap_SegmentReportingDisclosureTextBlock_a94e3070-e9b3-4541-8f54-1745a141b0c4_terseLabel_en-US" xlink:label="lab_us-gaap_SegmentReportingDisclosureTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Operating Segment Data</link:label>
    <link:label id="lab_us-gaap_SegmentReportingDisclosureTextBlock_label_en-US" xlink:label="lab_us-gaap_SegmentReportingDisclosureTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Segment Reporting Disclosure [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SegmentReportingDisclosureTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_SegmentReportingDisclosureTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_SegmentReportingDisclosureTextBlock" xlink:to="lab_us-gaap_SegmentReportingDisclosureTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LandAndBuildingMember_ab6b171a-20a0-42af-b2f1-cd9b2ca2d09d_terseLabel_en-US" xlink:label="lab_us-gaap_LandAndBuildingMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Buildings and Land [Member]</link:label>
    <link:label id="lab_us-gaap_LandAndBuildingMember_label_en-US" xlink:label="lab_us-gaap_LandAndBuildingMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Land and Building [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LandAndBuildingMember" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_LandAndBuildingMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LandAndBuildingMember" xlink:to="lab_us-gaap_LandAndBuildingMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_SubsegmentsConsolidationItemsAxis_132df56a-e584-40df-813e-49830836e5eb_terseLabel_en-US" xlink:label="lab_us-gaap_SubsegmentsConsolidationItemsAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Subsegments Consolidation Items [Axis]</link:label>
    <link:label id="lab_us-gaap_SubsegmentsConsolidationItemsAxis_label_en-US" xlink:label="lab_us-gaap_SubsegmentsConsolidationItemsAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Subsegments Consolidation Items [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SubsegmentsConsolidationItemsAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_SubsegmentsConsolidationItemsAxis"/>
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    <link:label id="lab_us-gaap_FairValueByMeasurementBasisAxis_cdc51ad4-d3e5-46a0-bf87-6c03da2cc59f_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueByMeasurementBasisAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Measurement Basis [Axis]</link:label>
    <link:label id="lab_us-gaap_FairValueByMeasurementBasisAxis_label_en-US" xlink:label="lab_us-gaap_FairValueByMeasurementBasisAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Measurement Basis [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueByMeasurementBasisAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_FairValueByMeasurementBasisAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FairValueByMeasurementBasisAxis" xlink:to="lab_us-gaap_FairValueByMeasurementBasisAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DeferredTaxLiabilitiesNetAbstract_0288ae63-04b7-4f45-8d0a-342fe5433007_terseLabel_en-US" xlink:label="lab_us-gaap_DeferredTaxLiabilitiesNetAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Deferred tax liabilities:</link:label>
    <link:label id="lab_us-gaap_DeferredTaxLiabilitiesNetAbstract_label_en-US" xlink:label="lab_us-gaap_DeferredTaxLiabilitiesNetAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Deferred Tax Liabilities, Net [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DeferredTaxLiabilitiesNetAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_DeferredTaxLiabilitiesNetAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DeferredTaxLiabilitiesNetAbstract" xlink:to="lab_us-gaap_DeferredTaxLiabilitiesNetAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_TrdArrIndTitle_terseLabel_en-US" xlink:label="lab_ecd_TrdArrIndTitle" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Title</link:label>
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    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_TrdArrIndTitle" xlink:to="lab_ecd_TrdArrIndTitle" xlink:type="arc" order="1"/>
    <link:label id="lab_codi_OtherIdentifiableAssets_5292e2bf-1468-43a4-ba12-eca8b8346cf2_terseLabel_en-US" xlink:label="lab_codi_OtherIdentifiableAssets" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Other Identifiable Assets</link:label>
    <link:label id="lab_codi_OtherIdentifiableAssets_label_en-US" xlink:label="lab_codi_OtherIdentifiableAssets" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Other Identifiable Assets</link:label>
    <link:label id="lab_codi_OtherIdentifiableAssets_documentation_en-US" xlink:label="lab_codi_OtherIdentifiableAssets" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Other Identifiable Assets</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_codi_OtherIdentifiableAssets" xlink:href="codi-20241231.xsd#codi_OtherIdentifiableAssets"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_codi_OtherIdentifiableAssets" xlink:to="lab_codi_OtherIdentifiableAssets" xlink:type="arc" order="1"/>
    <link:label id="lab_srt_ConsolidatedEntitiesAxis_ffb5c506-a046-466a-a72a-075e6dac10a3_terseLabel_en-US" xlink:label="lab_srt_ConsolidatedEntitiesAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Consolidated Entities [Axis]</link:label>
    <link:label id="lab_srt_ConsolidatedEntitiesAxis_label_en-US" xlink:label="lab_srt_ConsolidatedEntitiesAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Consolidated Entities [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_srt_ConsolidatedEntitiesAxis" xlink:href="https://xbrl.fasb.org/srt/2024/elts/srt-2024.xsd#srt_ConsolidatedEntitiesAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_srt_ConsolidatedEntitiesAxis" xlink:to="lab_srt_ConsolidatedEntitiesAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ScheduleOfIncomeBeforeIncomeTaxDomesticAndForeignTableTextBlock_56f1f54f-c1a2-400e-87ec-5216bd183472_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfIncomeBeforeIncomeTaxDomesticAndForeignTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Income before Income Tax, Domestic and Foreign</link:label>
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    <link:label id="lab_us-gaap_UnrecognizedTaxBenefits_a10c2bcd-8056-468f-94d9-36b39dda9316_terseLabel_en-US" xlink:label="lab_us-gaap_UnrecognizedTaxBenefits" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Unrecognized Tax Benefits</link:label>
    <link:label id="lab_us-gaap_UnrecognizedTaxBenefits_52314251-aa13-466b-a164-39acac377ae1_periodStartLabel_en-US" xlink:label="lab_us-gaap_UnrecognizedTaxBenefits" xlink:role="http://www.xbrl.org/2003/role/periodStartLabel" xlink:type="resource" xml:lang="en-US">Beginning balance</link:label>
    <link:label id="lab_us-gaap_UnrecognizedTaxBenefits_d6a834da-e54e-430a-8a36-d87828c4c56e_periodEndLabel_en-US" xlink:label="lab_us-gaap_UnrecognizedTaxBenefits" xlink:role="http://www.xbrl.org/2003/role/periodEndLabel" xlink:type="resource" xml:lang="en-US">Ending balance</link:label>
    <link:label id="lab_us-gaap_UnrecognizedTaxBenefits_label_en-US" xlink:label="lab_us-gaap_UnrecognizedTaxBenefits" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Unrecognized Tax Benefits</link:label>
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    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_UnrecognizedTaxBenefits" xlink:to="lab_us-gaap_UnrecognizedTaxBenefits" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_InternalRevenueServiceIRSMember_522c7716-069e-413b-a667-67e523453e06_terseLabel_en-US" xlink:label="lab_us-gaap_InternalRevenueServiceIRSMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Internal Revenue Service (IRS)</link:label>
    <link:label id="lab_us-gaap_InternalRevenueServiceIRSMember_label_en-US" xlink:label="lab_us-gaap_InternalRevenueServiceIRSMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Internal Revenue Service (IRS) [Member]</link:label>
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    <link:label id="lab_dei_CityAreaCode_5de79b8b-fadf-4abf-bfe1-f283ead02a21_terseLabel_en-US" xlink:label="lab_dei_CityAreaCode" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">City Area Code</link:label>
    <link:label id="lab_dei_CityAreaCode_label_en-US" xlink:label="lab_dei_CityAreaCode" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">City Area Code</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_CityAreaCode" xlink:href="https://xbrl.sec.gov/dei/2024/dei-2024.xsd#dei_CityAreaCode"/>
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    <link:label id="lab_us-gaap_DiscontinuedOperationTaxEffectOfDiscontinuedOperation_5a62952c-ea58-4108-a249-68fe9554316e_terseLabel_en-US" xlink:label="lab_us-gaap_DiscontinuedOperationTaxEffectOfDiscontinuedOperation" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Provision for income taxes</link:label>
    <link:label id="lab_us-gaap_DiscontinuedOperationTaxEffectOfDiscontinuedOperation_label_en-US" xlink:label="lab_us-gaap_DiscontinuedOperationTaxEffectOfDiscontinuedOperation" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Discontinued Operation, Tax Effect of Discontinued Operation</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DiscontinuedOperationTaxEffectOfDiscontinuedOperation" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_DiscontinuedOperationTaxEffectOfDiscontinuedOperation"/>
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    <link:label id="lab_us-gaap_LiabilitiesCurrentAbstract_132e4fc2-ab65-4e62-98c3-0a6b73d4a24c_terseLabel_en-US" xlink:label="lab_us-gaap_LiabilitiesCurrentAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Current liabilities:</link:label>
    <link:label id="lab_us-gaap_LiabilitiesCurrentAbstract_label_en-US" xlink:label="lab_us-gaap_LiabilitiesCurrentAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Liabilities, Current [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LiabilitiesCurrentAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_LiabilitiesCurrentAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LiabilitiesCurrentAbstract" xlink:to="lab_us-gaap_LiabilitiesCurrentAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_AuditorLocation_5a923ebb-66cb-4e6c-99f6-e1fd1474d343_terseLabel_en-US" xlink:label="lab_dei_AuditorLocation" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Auditor Location</link:label>
    <link:label id="lab_dei_AuditorLocation_label_en-US" xlink:label="lab_dei_AuditorLocation" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Auditor Location</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_AuditorLocation" xlink:href="https://xbrl.sec.gov/dei/2024/dei-2024.xsd#dei_AuditorLocation"/>
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    <link:label id="lab_us-gaap_DeferredTaxAssetsTaxDeferredExpenseReservesAndAccrualsAccruedLiabilities_1e25fba9-a510-4e8f-b803-a5779a111b2b_terseLabel_en-US" xlink:label="lab_us-gaap_DeferredTaxAssetsTaxDeferredExpenseReservesAndAccrualsAccruedLiabilities" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Accrued expenses</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DeferredTaxAssetsTaxDeferredExpenseReservesAndAccrualsAccruedLiabilities" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_DeferredTaxAssetsTaxDeferredExpenseReservesAndAccrualsAccruedLiabilities"/>
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    <link:label id="lab_codi_A5.11TacticalMember_a23ffda6-feff-4b56-9f95-988c890da95d_terseLabel_en-US" xlink:label="lab_codi_A5.11TacticalMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">5.11 Tactical</link:label>
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    <link:label id="lab_codi_ReceivablesTradeAndOtherAccountsReceivableAllowanceForDoubtfulAccountsPolicyTextBlock_documentation_en-US" xlink:label="lab_codi_ReceivablesTradeAndOtherAccountsReceivableAllowanceForDoubtfulAccountsPolicyTextBlock" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Receivables trade and other accounts receivable allowance for doubtful accounts.</link:label>
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    <link:label id="lab_us-gaap_BusinessCombinationContingentConsiderationLiability_8f0a23e1-1ae1-407e-ab0a-1b9c7bf9dea5_terseLabel_en-US" xlink:label="lab_us-gaap_BusinessCombinationContingentConsiderationLiability" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Contingent consideration</link:label>
    <link:label id="lab_us-gaap_BusinessCombinationContingentConsiderationLiability_label_en-US" xlink:label="lab_us-gaap_BusinessCombinationContingentConsiderationLiability" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Business Combination, Contingent Consideration, Liability</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_BusinessCombinationContingentConsiderationLiability" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_BusinessCombinationContingentConsiderationLiability"/>
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    <link:label id="lab_codi_A2022TermLoanMember_ae87c217-dc49-4398-9884-5ad878dcbc28_terseLabel_en-US" xlink:label="lab_codi_A2022TermLoanMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">2022 Term Loan</link:label>
    <link:label id="lab_codi_A2022TermLoanMember_label_en-US" xlink:label="lab_codi_A2022TermLoanMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">2022 Term Loan [Member]</link:label>
    <link:label id="lab_codi_A2022TermLoanMember_documentation_en-US" xlink:label="lab_codi_A2022TermLoanMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">2022 Term Loan</link:label>
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    <link:label id="lab_us-gaap_DisposalGroupClassificationDomain_bd38580b-e0b3-427d-9ef7-f2e246f02789_terseLabel_en-US" xlink:label="lab_us-gaap_DisposalGroupClassificationDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Disposal Group Classification [Domain]</link:label>
    <link:label id="lab_us-gaap_DisposalGroupClassificationDomain_label_en-US" xlink:label="lab_us-gaap_DisposalGroupClassificationDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Disposal Group Classification [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DisposalGroupClassificationDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_DisposalGroupClassificationDomain"/>
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    <link:label id="lab_us-gaap_RevenueRecognitionPolicyTextBlock_label_en-US" xlink:label="lab_us-gaap_RevenueRecognitionPolicyTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Revenue [Policy Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_RevenueRecognitionPolicyTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_RevenueRecognitionPolicyTextBlock"/>
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    <link:label id="lab_us-gaap_GainLossOnDispositionOfAssets1_d7fb26b6-13f0-453a-93cf-cf07f8426903_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_GainLossOnDispositionOfAssets1" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Gain (Loss) on Disposition of Assets</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_GainLossOnDispositionOfAssets1" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_GainLossOnDispositionOfAssets1"/>
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    <link:label id="lab_us-gaap_PreferredStockMember_bae483c9-bafe-45f3-bdc0-e8603258d75a_terseLabel_en-US" xlink:label="lab_us-gaap_PreferredStockMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Preferred Stock [Member]</link:label>
    <link:label id="lab_us-gaap_PreferredStockMember_label_en-US" xlink:label="lab_us-gaap_PreferredStockMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Preferred Stock [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PreferredStockMember" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_PreferredStockMember"/>
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    <link:label id="lab_codi_DeferredTaxAssetsAccountsReceivableAndAllowance_cd200a77-e26c-4f73-8039-572d9061bf1d_terseLabel_en-US" xlink:label="lab_codi_DeferredTaxAssetsAccountsReceivableAndAllowance" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Accounts receivable and allowances</link:label>
    <link:label id="lab_codi_DeferredTaxAssetsAccountsReceivableAndAllowance_label_en-US" xlink:label="lab_codi_DeferredTaxAssetsAccountsReceivableAndAllowance" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Deferred Tax Assets Accounts Receivable And Allowance</link:label>
    <link:label id="lab_codi_DeferredTaxAssetsAccountsReceivableAndAllowance_documentation_en-US" xlink:label="lab_codi_DeferredTaxAssetsAccountsReceivableAndAllowance" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Deferred tax assets accounts receivable and allowance.</link:label>
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    <link:label id="lab_us-gaap_PaymentsForRepurchaseOfCommonStock_4072acbf-fe74-4813-9d34-98fc7c554a3e_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_PaymentsForRepurchaseOfCommonStock" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Payments for Repurchase of Common Stock</link:label>
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    <link:label id="lab_us-gaap_ValuationAllowanceOfDeferredTaxAssetsMember_dc757761-fe53-46da-bd2f-207a6a3bdc08_terseLabel_en-US" xlink:label="lab_us-gaap_ValuationAllowanceOfDeferredTaxAssetsMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Valuation Allowance of Deferred Tax Assets</link:label>
    <link:label id="lab_us-gaap_ValuationAllowanceOfDeferredTaxAssetsMember_label_en-US" xlink:label="lab_us-gaap_ValuationAllowanceOfDeferredTaxAssetsMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">SEC Schedule, 12-09, Valuation Allowance, Deferred Tax Asset [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ValuationAllowanceOfDeferredTaxAssetsMember" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_ValuationAllowanceOfDeferredTaxAssetsMember"/>
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    <link:label id="lab_dei_DocumentInformationLineItems_db4901b2-6a88-42c7-ad21-49490311da20_terseLabel_en-US" xlink:label="lab_dei_DocumentInformationLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Document Information [Line Items]</link:label>
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    <link:label id="lab_us-gaap_PensionAndOtherPostretirementPlansPolicy_3293b5f4-bda7-4aaf-ade3-a0ee10ff0ed6_terseLabel_en-US" xlink:label="lab_us-gaap_PensionAndOtherPostretirementPlansPolicy" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Employee Retirement Plans</link:label>
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    <link:label id="lab_us-gaap_LongTermDebtNoncurrent_c0e2eb6c-ea33-408a-8fb2-90456399a20d_verboseLabel_en-US" xlink:label="lab_us-gaap_LongTermDebtNoncurrent" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Long-term debt</link:label>
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    <link:label id="lab_us-gaap_RetainedEarningsAccumulatedDeficit_label_en-US" xlink:label="lab_us-gaap_RetainedEarningsAccumulatedDeficit" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Retained Earnings (Accumulated Deficit)</link:label>
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    <link:label id="lab_us-gaap_FinanceLeaseRightOfUseAssetStatementOfFinancialPositionExtensibleList_label_en-US" xlink:label="lab_us-gaap_FinanceLeaseRightOfUseAssetStatementOfFinancialPositionExtensibleList" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Finance Lease, Right-of-Use Asset, Statement of Financial Position [Extensible Enumeration]</link:label>
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    <link:label id="lab_us-gaap_ClassOfStockDomain_3c7a79ca-a4d2-431d-8ca8-f209e02c71bd_terseLabel_en-US" xlink:label="lab_us-gaap_ClassOfStockDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Class of Stock [Domain]</link:label>
    <link:label id="lab_us-gaap_ClassOfStockDomain_label_en-US" xlink:label="lab_us-gaap_ClassOfStockDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Class of Stock [Domain]</link:label>
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    <link:label id="lab_us-gaap_RelatedPartyTransactionLineItems_label_en-US" xlink:label="lab_us-gaap_RelatedPartyTransactionLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Related Party Transaction [Line Items]</link:label>
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    <link:label id="lab_us-gaap_IncreaseDecreaseInInventories_label_en-US" xlink:label="lab_us-gaap_IncreaseDecreaseInInventories" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Increase (Decrease) in Inventories</link:label>
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    <link:label id="lab_us-gaap_DeferredFinanceCostsGross_be3ef596-b15c-4d38-beaa-32833b54f7df_terseLabel_en-US" xlink:label="lab_us-gaap_DeferredFinanceCostsGross" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Deferred debt issuance costs</link:label>
    <link:label id="lab_us-gaap_DeferredFinanceCostsGross_label_en-US" xlink:label="lab_us-gaap_DeferredFinanceCostsGross" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Issuance Costs, Gross</link:label>
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    <link:label id="lab_us-gaap_DeferredIncomeTaxesAndTaxCredits_9f62b3f8-554b-42e6-ba80-61b70a594fa1_terseLabel_en-US" xlink:label="lab_us-gaap_DeferredIncomeTaxesAndTaxCredits" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Deferred taxes</link:label>
    <link:label id="lab_us-gaap_DeferredIncomeTaxesAndTaxCredits_label_en-US" xlink:label="lab_us-gaap_DeferredIncomeTaxesAndTaxCredits" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Deferred Income Taxes and Tax Credits</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DeferredIncomeTaxesAndTaxCredits" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_DeferredIncomeTaxesAndTaxCredits"/>
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    <link:label id="lab_us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInYearTwo_5a809b53-3bec-416d-9892-cf8252eca8ca_terseLabel_en-US" xlink:label="lab_us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInYearTwo" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Long-Term Debt, Maturity, Year Two</link:label>
    <link:label id="lab_us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInYearTwo_label_en-US" xlink:label="lab_us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInYearTwo" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Long-Term Debt, Maturity, Year Two</link:label>
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    <link:label id="lab_ecd_TrdArrSecuritiesAggAvailAmt_terseLabel_en-US" xlink:label="lab_ecd_TrdArrSecuritiesAggAvailAmt" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Aggregate Available</link:label>
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    <link:label id="lab_us-gaap_OperatingLeaseLiability_b386a0b5-fce3-48ce-be15-134d49e9b43d_terseLabel_en-US" xlink:label="lab_us-gaap_OperatingLeaseLiability" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Present value of lease liabilities</link:label>
    <link:label id="lab_us-gaap_OperatingLeaseLiability_label_en-US" xlink:label="lab_us-gaap_OperatingLeaseLiability" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Operating Lease, Liability</link:label>
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    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OperatingLeaseLiability" xlink:to="lab_us-gaap_OperatingLeaseLiability" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_AwardUndrlygSecuritiesAmt_terseLabel_en-US" xlink:label="lab_ecd_AwardUndrlygSecuritiesAmt" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Underlying Securities</link:label>
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    <link:label id="lab_codi_TotalDebtToEbitdaRatio_ea6c05f8-ebfb-43bd-b9d4-259cb7afb1c8_terseLabel_en-US" xlink:label="lab_codi_TotalDebtToEbitdaRatio" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Total Debt To Ebitda Ratio</link:label>
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    <link:label id="lab_us-gaap_GeographicDistributionForeignMember_0e581bbe-4170-4feb-b47a-536a6b515898_terseLabel_en-US" xlink:label="lab_us-gaap_GeographicDistributionForeignMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Foreign</link:label>
    <link:label id="lab_us-gaap_GeographicDistributionForeignMember_label_en-US" xlink:label="lab_us-gaap_GeographicDistributionForeignMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Geographic Distribution, Foreign [Member]</link:label>
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    <link:label id="lab_us-gaap_FinanceLeaseLiabilityPaymentsDueYearFive_84e88ef6-b919-4f0a-970e-fc0136bf4ca9_terseLabel_en-US" xlink:label="lab_us-gaap_FinanceLeaseLiabilityPaymentsDueYearFive" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Finance Lease, Liability, to be Paid, Year Five</link:label>
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    <link:label id="lab_us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedCurrentAssetsReceivables_label_en-US" xlink:label="lab_us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedCurrentAssetsReceivables" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Business Combination, Recognized Identifiable Assets Acquired and Liabilities Assumed, Current Assets, Receivables</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedCurrentAssetsReceivables" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedCurrentAssetsReceivables"/>
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    <link:label id="lab_us-gaap_StockAppreciationRightsSARSMember_terseLabel_en-US" xlink:label="lab_us-gaap_StockAppreciationRightsSARSMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Stock Appreciation Rights (SARs)</link:label>
    <link:label id="lab_us-gaap_StockAppreciationRightsSARSMember_label_en-US" xlink:label="lab_us-gaap_StockAppreciationRightsSARSMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Stock Appreciation Rights (SARs) [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_StockAppreciationRightsSARSMember" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_StockAppreciationRightsSARSMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_StockAppreciationRightsSARSMember" xlink:to="lab_us-gaap_StockAppreciationRightsSARSMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_MachineryAndEquipmentMember_f6f158c7-863d-42be-8a16-9ba13041ab04_terseLabel_en-US" xlink:label="lab_us-gaap_MachineryAndEquipmentMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Machinery and equipment</link:label>
    <link:label id="lab_us-gaap_MachineryAndEquipmentMember_label_en-US" xlink:label="lab_us-gaap_MachineryAndEquipmentMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Machinery and Equipment [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_MachineryAndEquipmentMember" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_MachineryAndEquipmentMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_MachineryAndEquipmentMember" xlink:to="lab_us-gaap_MachineryAndEquipmentMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_SubsequentEventsAbstract_9d1f9c79-3397-4485-9763-9ec3b44bcda4_terseLabel_en-US" xlink:label="lab_us-gaap_SubsequentEventsAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Subsequent Events [Abstract]</link:label>
    <link:label id="lab_us-gaap_SubsequentEventsAbstract_label_en-US" xlink:label="lab_us-gaap_SubsequentEventsAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Subsequent Events [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SubsequentEventsAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_SubsequentEventsAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_SubsequentEventsAbstract" xlink:to="lab_us-gaap_SubsequentEventsAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DefinedBenefitPlanActualReturnOnPlanAssets_1c068d54-be4d-4bc2-8e82-08b0d07cf1df_terseLabel_en-US" xlink:label="lab_us-gaap_DefinedBenefitPlanActualReturnOnPlanAssets" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Actual return on plan assets</link:label>
    <link:label id="lab_us-gaap_DefinedBenefitPlanActualReturnOnPlanAssets_label_en-US" xlink:label="lab_us-gaap_DefinedBenefitPlanActualReturnOnPlanAssets" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Defined Benefit Plan, Plan Assets, Increase (Decrease) for Actual Return (Loss)</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DefinedBenefitPlanActualReturnOnPlanAssets" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_DefinedBenefitPlanActualReturnOnPlanAssets"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DefinedBenefitPlanActualReturnOnPlanAssets" xlink:to="lab_us-gaap_DefinedBenefitPlanActualReturnOnPlanAssets" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DeferredFinanceCostsNet_c383b478-c6cc-4ac6-9bb9-a95411b2baac_terseLabel_en-US" xlink:label="lab_us-gaap_DeferredFinanceCostsNet" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Deferred debt issuance costs, net</link:label>
    <link:label id="lab_us-gaap_DeferredFinanceCostsNet_label_en-US" xlink:label="lab_us-gaap_DeferredFinanceCostsNet" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Issuance Costs, Net</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DeferredFinanceCostsNet" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_DeferredFinanceCostsNet"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DeferredFinanceCostsNet" xlink:to="lab_us-gaap_DeferredFinanceCostsNet" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DebtDisclosureTextBlock_eee45f48-7a09-4643-aac5-48388bfa9d48_terseLabel_en-US" xlink:label="lab_us-gaap_DebtDisclosureTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Debt</link:label>
    <link:label id="lab_us-gaap_DebtDisclosureTextBlock_label_en-US" xlink:label="lab_us-gaap_DebtDisclosureTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Disclosure [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtDisclosureTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_DebtDisclosureTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DebtDisclosureTextBlock" xlink:to="lab_us-gaap_DebtDisclosureTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FairValueMeasurementsFairValueHierarchyDomain_d45a458a-4dae-4dc5-99f5-c59682eb3b8e_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueMeasurementsFairValueHierarchyDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Fair Value Hierarchy and NAV [Domain]</link:label>
    <link:label id="lab_us-gaap_FairValueMeasurementsFairValueHierarchyDomain_label_en-US" xlink:label="lab_us-gaap_FairValueMeasurementsFairValueHierarchyDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fair Value Hierarchy and NAV [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueMeasurementsFairValueHierarchyDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_FairValueMeasurementsFairValueHierarchyDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FairValueMeasurementsFairValueHierarchyDomain" xlink:to="lab_us-gaap_FairValueMeasurementsFairValueHierarchyDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_RecoveryOfErrCompDisclosureLineItems_label_en-US" xlink:label="lab_ecd_RecoveryOfErrCompDisclosureLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Recovery of Erroneously Awarded Compensation Disclosure [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_RecoveryOfErrCompDisclosureLineItems" xlink:href="https://xbrl.sec.gov/ecd/2024/ecd-2024.xsd#ecd_RecoveryOfErrCompDisclosureLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_RecoveryOfErrCompDisclosureLineItems" xlink:to="lab_ecd_RecoveryOfErrCompDisclosureLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DebtInstrumentFaceAmount_f73acecc-18f5-438a-92d1-8d5a1f32b0c1_terseLabel_en-US" xlink:label="lab_us-gaap_DebtInstrumentFaceAmount" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Letter of credit, aggregate face amount</link:label>
    <link:label id="lab_us-gaap_DebtInstrumentFaceAmount_label_en-US" xlink:label="lab_us-gaap_DebtInstrumentFaceAmount" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Instrument, Face Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtInstrumentFaceAmount" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_DebtInstrumentFaceAmount"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DebtInstrumentFaceAmount" xlink:to="lab_us-gaap_DebtInstrumentFaceAmount" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_TechnologyBasedIntangibleAssetsMember_d8fedfdd-4062-4805-a792-9b9c03e40125_terseLabel_en-US" xlink:label="lab_us-gaap_TechnologyBasedIntangibleAssetsMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Technology-Based Intangible Assets [Member]</link:label>
    <link:label id="lab_us-gaap_TechnologyBasedIntangibleAssetsMember_label_en-US" xlink:label="lab_us-gaap_TechnologyBasedIntangibleAssetsMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Technology-Based Intangible Assets [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_TechnologyBasedIntangibleAssetsMember" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_TechnologyBasedIntangibleAssetsMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_TechnologyBasedIntangibleAssetsMember" xlink:to="lab_us-gaap_TechnologyBasedIntangibleAssetsMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ProductWarrantyAccrual_397f866e-a0df-4125-9907-b36aedaef11e_terseLabel_en-US" xlink:label="lab_us-gaap_ProductWarrantyAccrual" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Warranty payable</link:label>
    <link:label id="lab_us-gaap_ProductWarrantyAccrual_label_en-US" xlink:label="lab_us-gaap_ProductWarrantyAccrual" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Standard and Extended Product Warranty Accrual</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ProductWarrantyAccrual" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_ProductWarrantyAccrual"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ProductWarrantyAccrual" xlink:to="lab_us-gaap_ProductWarrantyAccrual" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisLiabilitySettlements_c10a67df-8775-42b0-87b9-5c339174077b_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisLiabilitySettlements" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Fair Value, Measurement with Unobservable Inputs Reconciliation, Recurring Basis, Liability, Settlements</link:label>
    <link:label id="lab_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisLiabilitySettlements_label_en-US" xlink:label="lab_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisLiabilitySettlements" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fair Value, Measurement with Unobservable Inputs Reconciliation, Recurring Basis, Liability, Settlements</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisLiabilitySettlements" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisLiabilitySettlements"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisLiabilitySettlements" xlink:to="lab_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisLiabilitySettlements" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_EntityAddressPostalZipCode_e88fdde2-3661-44df-ab06-59c1aa74b1cb_terseLabel_en-US" xlink:label="lab_dei_EntityAddressPostalZipCode" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Entity Address, Postal Zip Code</link:label>
    <link:label id="lab_dei_EntityAddressPostalZipCode_label_en-US" xlink:label="lab_dei_EntityAddressPostalZipCode" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Entity Address, Postal Zip Code</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityAddressPostalZipCode" xlink:href="https://xbrl.sec.gov/dei/2024/dei-2024.xsd#dei_EntityAddressPostalZipCode"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_EntityAddressPostalZipCode" xlink:to="lab_dei_EntityAddressPostalZipCode" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AdvertisingExpense_f929368c-dcb2-4bef-ad8b-490d0c2b4d2c_terseLabel_en-US" xlink:label="lab_us-gaap_AdvertisingExpense" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Advertising costs</link:label>
    <link:label id="lab_us-gaap_AdvertisingExpense_label_en-US" xlink:label="lab_us-gaap_AdvertisingExpense" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Advertising Expense</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AdvertisingExpense" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_AdvertisingExpense"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AdvertisingExpense" xlink:to="lab_us-gaap_AdvertisingExpense" xlink:type="arc" order="1"/>
    <link:label id="lab_codi_BusinessCombinationIntegrationServicesPayable_e2aef3b1-da43-4e11-bd5c-bc74beb134b8_terseLabel_en-US" xlink:label="lab_codi_BusinessCombinationIntegrationServicesPayable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Integration service fees</link:label>
    <link:label id="lab_codi_BusinessCombinationIntegrationServicesPayable_label_en-US" xlink:label="lab_codi_BusinessCombinationIntegrationServicesPayable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Business Combination, Integration Services Payable</link:label>
    <link:label id="lab_codi_BusinessCombinationIntegrationServicesPayable_documentation_en-US" xlink:label="lab_codi_BusinessCombinationIntegrationServicesPayable" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Business Combination, Integration Services Payable</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_codi_BusinessCombinationIntegrationServicesPayable" xlink:href="codi-20241231.xsd#codi_BusinessCombinationIntegrationServicesPayable"/>
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    <link:label id="lab_us-gaap_BusinessCombinationIntegrationRelatedCosts_37841717-3963-487b-8ee4-e59f870c242a_terseLabel_en-US" xlink:label="lab_us-gaap_BusinessCombinationIntegrationRelatedCosts" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Integration service fees</link:label>
    <link:label id="lab_us-gaap_BusinessCombinationIntegrationRelatedCosts_label_en-US" xlink:label="lab_us-gaap_BusinessCombinationIntegrationRelatedCosts" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Business Combination, Integration Related Costs</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_BusinessCombinationIntegrationRelatedCosts" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_BusinessCombinationIntegrationRelatedCosts"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_BusinessCombinationIntegrationRelatedCosts" xlink:to="lab_us-gaap_BusinessCombinationIntegrationRelatedCosts" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CashAndCashEquivalentsAtCarryingValue_5758e48a-a7d9-4f74-9409-214fb90a2da1_terseLabel_en-US" xlink:label="lab_us-gaap_CashAndCashEquivalentsAtCarryingValue" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Cash and cash equivalents</link:label>
    <link:label id="lab_us-gaap_CashAndCashEquivalentsAtCarryingValue_label_en-US" xlink:label="lab_us-gaap_CashAndCashEquivalentsAtCarryingValue" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Cash and Cash Equivalents, at Carrying Value</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CashAndCashEquivalentsAtCarryingValue" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_CashAndCashEquivalentsAtCarryingValue"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CashAndCashEquivalentsAtCarryingValue" xlink:to="lab_us-gaap_CashAndCashEquivalentsAtCarryingValue" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_PaymentsForProceedsFromOtherInvestingActivities_ea67eea8-4313-42e9-9ea5-5cb94cfcb2d4_negatedLabel_en-US" xlink:label="lab_us-gaap_PaymentsForProceedsFromOtherInvestingActivities" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:type="resource" xml:lang="en-US">Other investing activities</link:label>
    <link:label id="lab_us-gaap_PaymentsForProceedsFromOtherInvestingActivities_label_en-US" xlink:label="lab_us-gaap_PaymentsForProceedsFromOtherInvestingActivities" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Payments for (Proceeds from) Other Investing Activities</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PaymentsForProceedsFromOtherInvestingActivities" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_PaymentsForProceedsFromOtherInvestingActivities"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PaymentsForProceedsFromOtherInvestingActivities" xlink:to="lab_us-gaap_PaymentsForProceedsFromOtherInvestingActivities" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OtherNoncurrentAssetsMember_ca92fc6f-4bff-480c-90a2-922935f7f783_terseLabel_en-US" xlink:label="lab_us-gaap_OtherNoncurrentAssetsMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Other noncurrent assets</link:label>
    <link:label id="lab_us-gaap_OtherNoncurrentAssetsMember_label_en-US" xlink:label="lab_us-gaap_OtherNoncurrentAssetsMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Other Noncurrent Assets [Member]</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_ecd_ChngInFrValOfOutsdngAndUnvstdEqtyAwrdsGrntdInPrrYrsMember" xlink:href="https://xbrl.sec.gov/ecd/2024/ecd-2024.xsd#ecd_ChngInFrValOfOutsdngAndUnvstdEqtyAwrdsGrntdInPrrYrsMember"/>
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    <link:label id="lab_us-gaap_CorporateJointVentureMember_f1c8f650-d1ed-4879-9ff7-44e212328189_terseLabel_en-US" xlink:label="lab_us-gaap_CorporateJointVentureMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Corporate Joint Venture</link:label>
    <link:label id="lab_us-gaap_CorporateJointVentureMember_label_en-US" xlink:label="lab_us-gaap_CorporateJointVentureMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Corporate Joint Venture [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CorporateJointVentureMember" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_CorporateJointVentureMember"/>
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    <link:label id="lab_us-gaap_ScheduleOfQuarterlyFinancialInformationTableTextBlock_95a6741c-345a-4acb-85fb-df7cb133f8f6_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfQuarterlyFinancialInformationTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Summary of Unaudited Quarterly Financial Data</link:label>
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    <link:label id="lab_dei_AuditorName_de651233-e0dc-4150-bc77-67151471e389_terseLabel_en-US" xlink:label="lab_dei_AuditorName" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Auditor Name</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_dei_AuditorName" xlink:href="https://xbrl.sec.gov/dei/2024/dei-2024.xsd#dei_AuditorName"/>
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    <link:label id="lab_codi_NetIncomeLossAvailabletoTrustStockNetofDistributions_726a4b65-f30c-472e-9082-95718eeb2fe5_terseLabel_en-US" xlink:label="lab_codi_NetIncomeLossAvailabletoTrustStockNetofDistributions" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Net Income Loss Available to Trust Stock Net of Distributions</link:label>
    <link:label id="lab_codi_NetIncomeLossAvailabletoTrustStockNetofDistributions_label_en-US" xlink:label="lab_codi_NetIncomeLossAvailabletoTrustStockNetofDistributions" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Net Income Loss Available to Trust Stock Net of Distributions</link:label>
    <link:label id="lab_codi_NetIncomeLossAvailabletoTrustStockNetofDistributions_documentation_en-US" xlink:label="lab_codi_NetIncomeLossAvailabletoTrustStockNetofDistributions" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Net Income Loss Available to Trust Stock Net of Distributions</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_codi_NetIncomeLossAvailabletoTrustStockNetofDistributions" xlink:href="codi-20241231.xsd#codi_NetIncomeLossAvailabletoTrustStockNetofDistributions"/>
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    <link:label id="lab_us-gaap_CurrentIncomeTaxExpenseBenefitContinuingOperationsAbstract_66ee33bc-e5e9-48c3-afd6-e29cfc2c9c33_terseLabel_en-US" xlink:label="lab_us-gaap_CurrentIncomeTaxExpenseBenefitContinuingOperationsAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Current taxes</link:label>
    <link:label id="lab_us-gaap_CurrentIncomeTaxExpenseBenefitContinuingOperationsAbstract_label_en-US" xlink:label="lab_us-gaap_CurrentIncomeTaxExpenseBenefitContinuingOperationsAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Current Income Tax Expense (Benefit), Continuing Operations [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CurrentIncomeTaxExpenseBenefitContinuingOperationsAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_CurrentIncomeTaxExpenseBenefitContinuingOperationsAbstract"/>
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    <link:label id="lab_us-gaap_GainsLossesOnExtinguishmentOfDebt_764520be-9182-4be8-a8d4-9dc13b5cebfe_terseLabel_en-US" xlink:label="lab_us-gaap_GainsLossesOnExtinguishmentOfDebt" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Loss on debt extinguishment</link:label>
    <link:label id="lab_us-gaap_GainsLossesOnExtinguishmentOfDebt_78d94f0e-632d-4df0-a61e-b2c29fa30adb_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_GainsLossesOnExtinguishmentOfDebt" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Loss on debt extinguishment</link:label>
    <link:label id="lab_us-gaap_GainsLossesOnExtinguishmentOfDebt_label_en-US" xlink:label="lab_us-gaap_GainsLossesOnExtinguishmentOfDebt" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Gain (Loss) on Extinguishment of Debt</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_GainsLossesOnExtinguishmentOfDebt" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_GainsLossesOnExtinguishmentOfDebt"/>
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    <link:label id="lab_us-gaap_NonmonetaryTransactionGrossOperatingRevenueRecognized_4caaf8ab-b4ee-4669-a69a-61ae79e0b55b_terseLabel_en-US" xlink:label="lab_us-gaap_NonmonetaryTransactionGrossOperatingRevenueRecognized" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Nonmonetary Transaction, Gross Operating Revenue Recognized</link:label>
    <link:label id="lab_us-gaap_NonmonetaryTransactionGrossOperatingRevenueRecognized_label_en-US" xlink:label="lab_us-gaap_NonmonetaryTransactionGrossOperatingRevenueRecognized" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Nonmonetary Transaction, Gross Operating Revenue Recognized</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_NonmonetaryTransactionGrossOperatingRevenueRecognized" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_NonmonetaryTransactionGrossOperatingRevenueRecognized"/>
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    <link:label id="lab_ecd_YrEndFrValOfEqtyAwrdsGrntdInCvrdYrOutsdngAndUnvstdMember_terseLabel_en-US" xlink:label="lab_ecd_YrEndFrValOfEqtyAwrdsGrntdInCvrdYrOutsdngAndUnvstdMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Year-end Fair Value of Equity Awards Granted in Covered Year that are Outstanding and Unvested</link:label>
    <link:label id="lab_ecd_YrEndFrValOfEqtyAwrdsGrntdInCvrdYrOutsdngAndUnvstdMember_label_en-US" xlink:label="lab_ecd_YrEndFrValOfEqtyAwrdsGrntdInCvrdYrOutsdngAndUnvstdMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Year-end Fair Value of Equity Awards Granted in Covered Year that are Outstanding and Unvested [Member]</link:label>
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    <link:label id="lab_us-gaap_PropertyPlantAndEquipmentUsefulLife_e607327d-84b2-47c3-81cb-fe30b586add5_terseLabel_en-US" xlink:label="lab_us-gaap_PropertyPlantAndEquipmentUsefulLife" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Useful life for property, plant and equipment, in years</link:label>
    <link:label id="lab_us-gaap_PropertyPlantAndEquipmentUsefulLife_label_en-US" xlink:label="lab_us-gaap_PropertyPlantAndEquipmentUsefulLife" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Property, Plant and Equipment, Useful Life</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PropertyPlantAndEquipmentUsefulLife" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_PropertyPlantAndEquipmentUsefulLife"/>
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    <link:label id="lab_us-gaap_MinorityInterestDisclosureTextBlock_c6a7eaa2-9572-4bcf-868d-e984e73605d0_terseLabel_en-US" xlink:label="lab_us-gaap_MinorityInterestDisclosureTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Noncontrolling Interest</link:label>
    <link:label id="lab_us-gaap_MinorityInterestDisclosureTextBlock_label_en-US" xlink:label="lab_us-gaap_MinorityInterestDisclosureTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Noncontrolling Interest Disclosure [Text Block]</link:label>
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    <link:label id="lab_us-gaap_FairValueDisclosureItemAmountsDomain_0a0cfe85-f3f5-425f-9e22-4fa0e509145f_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueDisclosureItemAmountsDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Fair Value Measurement [Domain]</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueDisclosureItemAmountsDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_FairValueDisclosureItemAmountsDomain"/>
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    <link:label id="lab_us-gaap_CashAcquiredFromAcquisition_491b1882-f97f-4be7-accf-891fb6dbe64a_terseLabel_en-US" xlink:label="lab_us-gaap_CashAcquiredFromAcquisition" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Cash Acquired from Acquisition</link:label>
    <link:label id="lab_us-gaap_CashAcquiredFromAcquisition_99eb339f-fef4-42b8-9212-171e68aeb5d6_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_CashAcquiredFromAcquisition" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Cash</link:label>
    <link:label id="lab_us-gaap_CashAcquiredFromAcquisition_label_en-US" xlink:label="lab_us-gaap_CashAcquiredFromAcquisition" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Cash Acquired from Acquisition</link:label>
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    <link:label id="lab_ecd_AdjToPeoCompFnTextBlock_terseLabel_en-US" xlink:label="lab_ecd_AdjToPeoCompFnTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Adjustment To PEO Compensation, Footnote</link:label>
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    <link:label id="lab_codi_PropertyPlantAndEquipmentUsefulLivesTableTextBlock_ad9aef5d-cb77-436e-a4c0-96d39e44afd7_terseLabel_en-US" xlink:label="lab_codi_PropertyPlantAndEquipmentUsefulLivesTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Summary of Ranges of Useful Lives</link:label>
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    <link:label id="lab_codi_PropertyPlantAndEquipmentAndInventoryTextBlock_51a5d948-3501-444d-bd9b-73373d2e103f_terseLabel_en-US" xlink:label="lab_codi_PropertyPlantAndEquipmentAndInventoryTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Inventory, Property, Plant and Equipment</link:label>
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    <link:label id="lab_us-gaap_FinanceLeasePrincipalPayments_aaf4cfc3-0d10-45d8-bf1f-636cd8d268ba_terseLabel_en-US" xlink:label="lab_us-gaap_FinanceLeasePrincipalPayments" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Finance Lease, Principal Payments</link:label>
    <link:label id="lab_us-gaap_FinanceLeasePrincipalPayments_label_en-US" xlink:label="lab_us-gaap_FinanceLeasePrincipalPayments" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Finance Lease, Principal Payments</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FinanceLeasePrincipalPayments" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_FinanceLeasePrincipalPayments"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FinanceLeasePrincipalPayments" xlink:to="lab_us-gaap_FinanceLeasePrincipalPayments" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_EffectiveIncomeTaxRateReconciliationNondeductibleExpense_9084d458-0d04-43f1-a5c1-bef2077987ac_terseLabel_en-US" xlink:label="lab_us-gaap_EffectiveIncomeTaxRateReconciliationNondeductibleExpense" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Effective Income Tax Rate Reconciliation, Nondeductible Expense, Percent</link:label>
    <link:label id="lab_us-gaap_EffectiveIncomeTaxRateReconciliationNondeductibleExpense_label_en-US" xlink:label="lab_us-gaap_EffectiveIncomeTaxRateReconciliationNondeductibleExpense" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Effective Income Tax Rate Reconciliation, Nondeductible Expense, Percent</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_EffectiveIncomeTaxRateReconciliationNondeductibleExpense" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_EffectiveIncomeTaxRateReconciliationNondeductibleExpense"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_EffectiveIncomeTaxRateReconciliationNondeductibleExpense" xlink:to="lab_us-gaap_EffectiveIncomeTaxRateReconciliationNondeductibleExpense" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_CompActuallyPaidVsOtherMeasureTextBlock_terseLabel_en-US" xlink:label="lab_ecd_CompActuallyPaidVsOtherMeasureTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Compensation Actually Paid vs. Other Measure</link:label>
    <link:label id="lab_ecd_CompActuallyPaidVsOtherMeasureTextBlock_label_en-US" xlink:label="lab_ecd_CompActuallyPaidVsOtherMeasureTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Compensation Actually Paid vs. Other Measure [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_CompActuallyPaidVsOtherMeasureTextBlock" xlink:href="https://xbrl.sec.gov/ecd/2024/ecd-2024.xsd#ecd_CompActuallyPaidVsOtherMeasureTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_CompActuallyPaidVsOtherMeasureTextBlock" xlink:to="lab_ecd_CompActuallyPaidVsOtherMeasureTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DefinedBenefitPlanForeignCurrencyExchangeRateChangesBenefitObligation_3f011ca5-0a2c-41ca-a2e8-2ebcdc73021c_terseLabel_en-US" xlink:label="lab_us-gaap_DefinedBenefitPlanForeignCurrencyExchangeRateChangesBenefitObligation" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Foreign currency translation</link:label>
    <link:label id="lab_us-gaap_DefinedBenefitPlanForeignCurrencyExchangeRateChangesBenefitObligation_label_en-US" xlink:label="lab_us-gaap_DefinedBenefitPlanForeignCurrencyExchangeRateChangesBenefitObligation" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Defined Benefit Plan, Benefit Obligation, Foreign Currency Translation Gain (Loss)</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DefinedBenefitPlanForeignCurrencyExchangeRateChangesBenefitObligation" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_DefinedBenefitPlanForeignCurrencyExchangeRateChangesBenefitObligation"/>
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    <link:label id="lab_us-gaap_ScheduleOfStockByClassTable_24e3e4d4-24fe-4fb5-b904-ca5a7c51a178_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfStockByClassTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Stock, Class of Stock [Table]</link:label>
    <link:label id="lab_us-gaap_ScheduleOfStockByClassTable_label_en-US" xlink:label="lab_us-gaap_ScheduleOfStockByClassTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Stock, Class of Stock [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfStockByClassTable" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_ScheduleOfStockByClassTable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ScheduleOfStockByClassTable" xlink:to="lab_us-gaap_ScheduleOfStockByClassTable" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_VstngDtFrValOfEqtyAwrdsGrntdAndVstdInCvrdYrMember_terseLabel_en-US" xlink:label="lab_ecd_VstngDtFrValOfEqtyAwrdsGrntdAndVstdInCvrdYrMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Vesting Date Fair Value of Equity Awards Granted and Vested in Covered Year</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_ecd_VstngDtFrValOfEqtyAwrdsGrntdAndVstdInCvrdYrMember" xlink:href="https://xbrl.sec.gov/ecd/2024/ecd-2024.xsd#ecd_VstngDtFrValOfEqtyAwrdsGrntdAndVstdInCvrdYrMember"/>
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    <link:label id="lab_us-gaap_Assets_360db524-f68c-443f-b484-b8cab2a5c524_totalLabel_en-US" xlink:label="lab_us-gaap_Assets" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Total assets</link:label>
    <link:label id="lab_us-gaap_Assets_d474dbec-aa8a-4866-874f-e227fbb953b0_terseLabel_en-US" xlink:label="lab_us-gaap_Assets" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Assets</link:label>
    <link:label id="lab_us-gaap_Assets_label_en-US" xlink:label="lab_us-gaap_Assets" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Assets</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_Assets" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_Assets"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_Assets" xlink:to="lab_us-gaap_Assets" xlink:type="arc" order="1"/>
    <link:label id="lab_srt_BoardOfDirectorsChairmanMember_7eeac196-cb52-4734-8095-b60f07d45576_terseLabel_en-US" xlink:label="lab_srt_BoardOfDirectorsChairmanMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Board of Directors Chairman</link:label>
    <link:label id="lab_srt_BoardOfDirectorsChairmanMember_label_en-US" xlink:label="lab_srt_BoardOfDirectorsChairmanMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Board of Directors Chairman [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_srt_BoardOfDirectorsChairmanMember" xlink:href="https://xbrl.fasb.org/srt/2024/elts/srt-2024.xsd#srt_BoardOfDirectorsChairmanMember"/>
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    <link:label id="lab_us-gaap_HedgeFundsEquityMember_80c0bd1b-1a1b-4c94-b6d2-090fc74ab143_terseLabel_en-US" xlink:label="lab_us-gaap_HedgeFundsEquityMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Hedge Funds, Equity [Member]</link:label>
    <link:label id="lab_us-gaap_HedgeFundsEquityMember_label_en-US" xlink:label="lab_us-gaap_HedgeFundsEquityMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Hedge Funds, Equity [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_HedgeFundsEquityMember" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_HedgeFundsEquityMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_HedgeFundsEquityMember" xlink:to="lab_us-gaap_HedgeFundsEquityMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CostOfGoodsAndServicesSold_b3a10c26-c9e8-4f29-a3f6-a343087c694f_terseLabel_en-US" xlink:label="lab_us-gaap_CostOfGoodsAndServicesSold" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Cost of revenues</link:label>
    <link:label id="lab_us-gaap_CostOfGoodsAndServicesSold_label_en-US" xlink:label="lab_us-gaap_CostOfGoodsAndServicesSold" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Cost of Goods and Services Sold</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CostOfGoodsAndServicesSold" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_CostOfGoodsAndServicesSold"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CostOfGoodsAndServicesSold" xlink:to="lab_us-gaap_CostOfGoodsAndServicesSold" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AdvertisingCostsPolicyTextBlock_58083a27-b660-4b88-ba3b-221d7bc2bffe_terseLabel_en-US" xlink:label="lab_us-gaap_AdvertisingCostsPolicyTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Advertising Costs</link:label>
    <link:label id="lab_us-gaap_AdvertisingCostsPolicyTextBlock_label_en-US" xlink:label="lab_us-gaap_AdvertisingCostsPolicyTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Advertising Cost [Policy Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AdvertisingCostsPolicyTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_AdvertisingCostsPolicyTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AdvertisingCostsPolicyTextBlock" xlink:to="lab_us-gaap_AdvertisingCostsPolicyTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_PaymentsToAcquirePropertyPlantAndEquipment_6e2a1d1a-81d5-4c47-84ce-98b9eacf814d_negatedLabel_en-US" xlink:label="lab_us-gaap_PaymentsToAcquirePropertyPlantAndEquipment" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:type="resource" xml:lang="en-US">Purchases of property and equipment</link:label>
    <link:label id="lab_us-gaap_PaymentsToAcquirePropertyPlantAndEquipment_label_en-US" xlink:label="lab_us-gaap_PaymentsToAcquirePropertyPlantAndEquipment" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Payments to Acquire Property, Plant, and Equipment</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PaymentsToAcquirePropertyPlantAndEquipment" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_PaymentsToAcquirePropertyPlantAndEquipment"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PaymentsToAcquirePropertyPlantAndEquipment" xlink:to="lab_us-gaap_PaymentsToAcquirePropertyPlantAndEquipment" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OtherLiabilitiesNoncurrent_109b65fa-cdd4-4401-b498-25e6b05413e1_terseLabel_en-US" xlink:label="lab_us-gaap_OtherLiabilitiesNoncurrent" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Other non-current liabilities</link:label>
    <link:label id="lab_us-gaap_OtherLiabilitiesNoncurrent_label_en-US" xlink:label="lab_us-gaap_OtherLiabilitiesNoncurrent" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Other Liabilities, Noncurrent</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OtherLiabilitiesNoncurrent" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_OtherLiabilitiesNoncurrent"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OtherLiabilitiesNoncurrent" xlink:to="lab_us-gaap_OtherLiabilitiesNoncurrent" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_MovementInStandardProductWarrantyAccrualRollForward_1fc5c9eb-3c6b-456c-89f4-d59fd3ba8c13_terseLabel_en-US" xlink:label="lab_us-gaap_MovementInStandardProductWarrantyAccrualRollForward" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Warranty liability:</link:label>
    <link:label id="lab_us-gaap_MovementInStandardProductWarrantyAccrualRollForward_label_en-US" xlink:label="lab_us-gaap_MovementInStandardProductWarrantyAccrualRollForward" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Movement in Standard Product Warranty Accrual [Roll Forward]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_MovementInStandardProductWarrantyAccrualRollForward" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_MovementInStandardProductWarrantyAccrualRollForward"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_MovementInStandardProductWarrantyAccrualRollForward" xlink:to="lab_us-gaap_MovementInStandardProductWarrantyAccrualRollForward" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_ForgoneRecoveryDueToViolationOfHomeCountryLawAmt_terseLabel_en-US" xlink:label="lab_ecd_ForgoneRecoveryDueToViolationOfHomeCountryLawAmt" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Forgone Recovery due to Violation of Home Country Law, Amount</link:label>
    <link:label id="lab_ecd_ForgoneRecoveryDueToViolationOfHomeCountryLawAmt_label_en-US" xlink:label="lab_ecd_ForgoneRecoveryDueToViolationOfHomeCountryLawAmt" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Forgone Recovery due to Violation of Home Country Law, Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_ForgoneRecoveryDueToViolationOfHomeCountryLawAmt" xlink:href="https://xbrl.sec.gov/ecd/2024/ecd-2024.xsd#ecd_ForgoneRecoveryDueToViolationOfHomeCountryLawAmt"/>
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    <link:label id="lab_us-gaap_ShareBasedCompensationOptionAndIncentivePlansPolicy_b71992c6-fa35-450f-bc23-9a2209b26605_terseLabel_en-US" xlink:label="lab_us-gaap_ShareBasedCompensationOptionAndIncentivePlansPolicy" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Stock Based Compensation</link:label>
    <link:label id="lab_us-gaap_ShareBasedCompensationOptionAndIncentivePlansPolicy_label_en-US" xlink:label="lab_us-gaap_ShareBasedCompensationOptionAndIncentivePlansPolicy" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Share-Based Payment Arrangement [Policy Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ShareBasedCompensationOptionAndIncentivePlansPolicy" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_ShareBasedCompensationOptionAndIncentivePlansPolicy"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ShareBasedCompensationOptionAndIncentivePlansPolicy" xlink:to="lab_us-gaap_ShareBasedCompensationOptionAndIncentivePlansPolicy" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ScheduleOfEffectiveIncomeTaxRateReconciliationTableTextBlock_ffb8104c-e2e1-4aae-91f9-f98cf26eb6bd_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfEffectiveIncomeTaxRateReconciliationTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Reconciliation Between Federal Statutory Rate and Effective Income Tax Rate</link:label>
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    <link:label id="lab_us-gaap_EquitySecuritiesByInvestmentObjectiveAxis_64e2ed55-a852-4393-a3d9-e646ac8aaf9e_terseLabel_en-US" xlink:label="lab_us-gaap_EquitySecuritiesByInvestmentObjectiveAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Investment Objective [Axis]</link:label>
    <link:label id="lab_us-gaap_EquitySecuritiesByInvestmentObjectiveAxis_label_en-US" xlink:label="lab_us-gaap_EquitySecuritiesByInvestmentObjectiveAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Investment Objective [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_EquitySecuritiesByInvestmentObjectiveAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_EquitySecuritiesByInvestmentObjectiveAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_EquitySecuritiesByInvestmentObjectiveAxis" xlink:to="lab_us-gaap_EquitySecuritiesByInvestmentObjectiveAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_codi_ActualDebtToEbitdaRatio_60fd6db2-07cd-440e-90c0-5fb14424a61f_terseLabel_en-US" xlink:label="lab_codi_ActualDebtToEbitdaRatio" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Actual Debt To Ebitda Ratio</link:label>
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    <link:label id="lab_codi_ActualDebtToEbitdaRatio_documentation_en-US" xlink:label="lab_codi_ActualDebtToEbitdaRatio" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Actual debt to EBITDA ratio.</link:label>
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    <link:label id="lab_ecd_TrdArrTerminationDate_terseLabel_en-US" xlink:label="lab_ecd_TrdArrTerminationDate" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Termination Date</link:label>
    <link:label id="lab_ecd_TrdArrTerminationDate_label_en-US" xlink:label="lab_ecd_TrdArrTerminationDate" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Trading Arrangement Termination Date</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_TrdArrTerminationDate" xlink:href="https://xbrl.sec.gov/ecd/2024/ecd-2024.xsd#ecd_TrdArrTerminationDate"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_TrdArrTerminationDate" xlink:to="lab_ecd_TrdArrTerminationDate" xlink:type="arc" order="1"/>
    <link:label id="lab_codi_ScheduleOfOtherRelatedPartyTransactionsLineItems_66f99788-5766-4e79-a77a-bfcaaeba8359_terseLabel_en-US" xlink:label="lab_codi_ScheduleOfOtherRelatedPartyTransactionsLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Other Related Party Transactions [Line Items]</link:label>
    <link:label id="lab_codi_ScheduleOfOtherRelatedPartyTransactionsLineItems_label_en-US" xlink:label="lab_codi_ScheduleOfOtherRelatedPartyTransactionsLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Schedule Of Other Related Party Transactions [Line Items]</link:label>
    <link:label id="lab_codi_ScheduleOfOtherRelatedPartyTransactionsLineItems_documentation_en-US" xlink:label="lab_codi_ScheduleOfOtherRelatedPartyTransactionsLineItems" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Schedule of Other Related Party Transactions [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_codi_ScheduleOfOtherRelatedPartyTransactionsLineItems" xlink:href="codi-20241231.xsd#codi_ScheduleOfOtherRelatedPartyTransactionsLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_codi_ScheduleOfOtherRelatedPartyTransactionsLineItems" xlink:to="lab_codi_ScheduleOfOtherRelatedPartyTransactionsLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ScheduleOfRelatedPartyTransactionsByRelatedPartyTable_85885cca-7ae6-4380-bdff-fbd3dc8ac11f_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfRelatedPartyTransactionsByRelatedPartyTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Related Party Transaction [Table]</link:label>
    <link:label id="lab_us-gaap_ScheduleOfRelatedPartyTransactionsByRelatedPartyTable_label_en-US" xlink:label="lab_us-gaap_ScheduleOfRelatedPartyTransactionsByRelatedPartyTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Related Party Transaction [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfRelatedPartyTransactionsByRelatedPartyTable" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_ScheduleOfRelatedPartyTransactionsByRelatedPartyTable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ScheduleOfRelatedPartyTransactionsByRelatedPartyTable" xlink:to="lab_us-gaap_ScheduleOfRelatedPartyTransactionsByRelatedPartyTable" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisLineItems_623d7d42-febd-4290-aa67-5e8adb5d9acc_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]</link:label>
    <link:label id="lab_us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisLineItems_label_en-US" xlink:label="lab_us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisLineItems" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisLineItems" xlink:to="lab_us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearTwo_d58f3245-180b-41f5-84c5-256d470b80ae_terseLabel_en-US" xlink:label="lab_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearTwo" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">2021</link:label>
    <link:label id="lab_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearTwo_label_en-US" xlink:label="lab_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearTwo" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Lessee, Operating Lease, Liability, to be Paid, Year Two</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearTwo" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearTwo"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearTwo" xlink:to="lab_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearTwo" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInNextTwelveMonths_1cae74b6-9f9e-4cf3-992e-759ecb3fb97f_terseLabel_en-US" xlink:label="lab_us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInNextTwelveMonths" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Long-Term Debt, Maturity, Year One</link:label>
    <link:label id="lab_us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInNextTwelveMonths_label_en-US" xlink:label="lab_us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInNextTwelveMonths" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Long-Term Debt, Maturity, Year One</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInNextTwelveMonths" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInNextTwelveMonths"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInNextTwelveMonths" xlink:to="lab_us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInNextTwelveMonths" xlink:type="arc" order="1"/>
    <link:label id="lab_codi_BusinessCombinationProvisionalInformationInitialAccountingIncompleteAdjustmentAccountsReceivable_f95110cd-bd09-4ea5-bacc-52ead355ad58_terseLabel_en-US" xlink:label="lab_codi_BusinessCombinationProvisionalInformationInitialAccountingIncompleteAdjustmentAccountsReceivable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Business Combination, Provisional Information, Initial Accounting Incomplete, Adjustment, Accounts Receivable</link:label>
    <link:label id="lab_codi_BusinessCombinationProvisionalInformationInitialAccountingIncompleteAdjustmentAccountsReceivable_label_en-US" xlink:label="lab_codi_BusinessCombinationProvisionalInformationInitialAccountingIncompleteAdjustmentAccountsReceivable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Business Combination, Provisional Information, Initial Accounting Incomplete, Adjustment, Accounts Receivable</link:label>
    <link:label id="lab_codi_BusinessCombinationProvisionalInformationInitialAccountingIncompleteAdjustmentAccountsReceivable_documentation_en-US" xlink:label="lab_codi_BusinessCombinationProvisionalInformationInitialAccountingIncompleteAdjustmentAccountsReceivable" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Business Combination, Provisional Information, Initial Accounting Incomplete, Adjustment, Accounts Receivable</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_codi_BusinessCombinationProvisionalInformationInitialAccountingIncompleteAdjustmentAccountsReceivable" xlink:href="codi-20241231.xsd#codi_BusinessCombinationProvisionalInformationInitialAccountingIncompleteAdjustmentAccountsReceivable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_codi_BusinessCombinationProvisionalInformationInitialAccountingIncompleteAdjustmentAccountsReceivable" xlink:to="lab_codi_BusinessCombinationProvisionalInformationInitialAccountingIncompleteAdjustmentAccountsReceivable" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedAssetsAbstract_9a5456fa-c0e8-4e97-882a-f8c4b99d6a62_terseLabel_en-US" xlink:label="lab_us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedAssetsAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Assets:</link:label>
    <link:label id="lab_us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedAssetsAbstract_label_en-US" xlink:label="lab_us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedAssetsAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Business Combination, Recognized Identifiable Assets Acquired and Liabilities Assumed, Assets [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedAssetsAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedAssetsAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedAssetsAbstract" xlink:to="lab_us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedAssetsAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DebtInstrumentAxis_b9141403-e96b-49f1-9948-54a4f50b562e_terseLabel_en-US" xlink:label="lab_us-gaap_DebtInstrumentAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Debt Instrument [Axis]</link:label>
    <link:label id="lab_us-gaap_DebtInstrumentAxis_label_en-US" xlink:label="lab_us-gaap_DebtInstrumentAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Instrument [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtInstrumentAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_DebtInstrumentAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DebtInstrumentAxis" xlink:to="lab_us-gaap_DebtInstrumentAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_codi_IdentifiableAssetsTotalIncludingOtherIdentifiableAssets_2547fa78-2a89-4e01-bba2-919bcbd33d34_terseLabel_en-US" xlink:label="lab_codi_IdentifiableAssetsTotalIncludingOtherIdentifiableAssets" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Identifiable Assets, Total, Including Other Identifiable Assets</link:label>
    <link:label id="lab_codi_IdentifiableAssetsTotalIncludingOtherIdentifiableAssets_label_en-US" xlink:label="lab_codi_IdentifiableAssetsTotalIncludingOtherIdentifiableAssets" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Identifiable Assets, Total, Including Other Identifiable Assets</link:label>
    <link:label id="lab_codi_IdentifiableAssetsTotalIncludingOtherIdentifiableAssets_documentation_en-US" xlink:label="lab_codi_IdentifiableAssetsTotalIncludingOtherIdentifiableAssets" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Identifiable Assets, Total, Including Other Identifiable Assets</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_codi_IdentifiableAssetsTotalIncludingOtherIdentifiableAssets" xlink:href="codi-20241231.xsd#codi_IdentifiableAssetsTotalIncludingOtherIdentifiableAssets"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_codi_IdentifiableAssetsTotalIncludingOtherIdentifiableAssets" xlink:to="lab_codi_IdentifiableAssetsTotalIncludingOtherIdentifiableAssets" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_NoncontrollingInterestAbstract_132ab71b-fb2f-4f31-97d4-9c61683af616_terseLabel_en-US" xlink:label="lab_us-gaap_NoncontrollingInterestAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Noncontrolling Interest [Abstract]</link:label>
    <link:label id="lab_us-gaap_NoncontrollingInterestAbstract_label_en-US" xlink:label="lab_us-gaap_NoncontrollingInterestAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Noncontrolling Interest [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_NoncontrollingInterestAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_NoncontrollingInterestAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_NoncontrollingInterestAbstract" xlink:to="lab_us-gaap_NoncontrollingInterestAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DefinedBenefitPlanFundedStatusOfPlanAbstract_4a54f718-4fa2-4e18-b1a9-d370a3926c89_terseLabel_en-US" xlink:label="lab_us-gaap_DefinedBenefitPlanFundedStatusOfPlanAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Change in benefit obligation:</link:label>
    <link:label id="lab_us-gaap_DefinedBenefitPlanFundedStatusOfPlanAbstract_label_en-US" xlink:label="lab_us-gaap_DefinedBenefitPlanFundedStatusOfPlanAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Defined Benefit Plan, Funded (Unfunded) Status of Plan [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DefinedBenefitPlanFundedStatusOfPlanAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_DefinedBenefitPlanFundedStatusOfPlanAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DefinedBenefitPlanFundedStatusOfPlanAbstract" xlink:to="lab_us-gaap_DefinedBenefitPlanFundedStatusOfPlanAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OtherOperatingIncomeExpenseNet_94082dd2-2f13-40d1-9a98-19c23522e4ab_totalLabel_en-US" xlink:label="lab_us-gaap_OtherOperatingIncomeExpenseNet" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Other expense, net</link:label>
    <link:label id="lab_us-gaap_OtherOperatingIncomeExpenseNet_label_en-US" xlink:label="lab_us-gaap_OtherOperatingIncomeExpenseNet" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Other Operating Income (Expense), Net</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OtherOperatingIncomeExpenseNet" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_OtherOperatingIncomeExpenseNet"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OtherOperatingIncomeExpenseNet" xlink:to="lab_us-gaap_OtherOperatingIncomeExpenseNet" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_NetIncomeLoss_4ce3f938-029a-4661-8223-6271a138166e_totalLabel_en-US" xlink:label="lab_us-gaap_NetIncomeLoss" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Net income attributable to Holdings</link:label>
    <link:label id="lab_us-gaap_NetIncomeLoss_44616198-f65a-4b37-89fb-432b3cf76270_terseLabel_en-US" xlink:label="lab_us-gaap_NetIncomeLoss" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Net income attributable to Holdings</link:label>
    <link:label id="lab_us-gaap_NetIncomeLoss_8503ed98-7a61-4864-a6e1-f23ea581f2ff_verboseLabel_en-US" xlink:label="lab_us-gaap_NetIncomeLoss" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Net income (loss) attributable to Holdings</link:label>
    <link:label id="lab_us-gaap_NetIncomeLoss_label_en-US" xlink:label="lab_us-gaap_NetIncomeLoss" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Net Income (Loss) Attributable to Parent</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_NetIncomeLoss" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_NetIncomeLoss"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_NetIncomeLoss" xlink:to="lab_us-gaap_NetIncomeLoss" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_TradingArrAxis_terseLabel_en-US" xlink:label="lab_ecd_TradingArrAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Trading Arrangement:</link:label>
    <link:label id="lab_ecd_TradingArrAxis_label_en-US" xlink:label="lab_ecd_TradingArrAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Trading Arrangement [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_TradingArrAxis" xlink:href="https://xbrl.sec.gov/ecd/2024/ecd-2024.xsd#ecd_TradingArrAxis"/>
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    <link:label id="lab_us-gaap_DefinedBenefitPlanExpectedFutureBenefitPaymentsFiveFiscalYearsThereafter_839536af-1bbc-4b34-8892-e649252436a5_terseLabel_en-US" xlink:label="lab_us-gaap_DefinedBenefitPlanExpectedFutureBenefitPaymentsFiveFiscalYearsThereafter" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Thereafter</link:label>
    <link:label id="lab_us-gaap_DefinedBenefitPlanExpectedFutureBenefitPaymentsFiveFiscalYearsThereafter_label_en-US" xlink:label="lab_us-gaap_DefinedBenefitPlanExpectedFutureBenefitPaymentsFiveFiscalYearsThereafter" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Defined Benefit Plan, Expected Future Benefit Payment, after Year Five for Next Five Years</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DefinedBenefitPlanExpectedFutureBenefitPaymentsFiveFiscalYearsThereafter" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_DefinedBenefitPlanExpectedFutureBenefitPaymentsFiveFiscalYearsThereafter"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DefinedBenefitPlanExpectedFutureBenefitPaymentsFiveFiscalYearsThereafter" xlink:to="lab_us-gaap_DefinedBenefitPlanExpectedFutureBenefitPaymentsFiveFiscalYearsThereafter" xlink:type="arc" order="1"/>
    <link:label id="lab_codi_NoncontrollingStockholderChargesAndOther_6e27835e-5614-47e1-b3d3-3d300f1cbcc5_terseLabel_en-US" xlink:label="lab_codi_NoncontrollingStockholderChargesAndOther" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Noncontrolling stockholder stock based compensation</link:label>
    <link:label id="lab_codi_NoncontrollingStockholderChargesAndOther_label_en-US" xlink:label="lab_codi_NoncontrollingStockholderChargesAndOther" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Noncontrolling Stockholder Charges And Other</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_codi_NoncontrollingStockholderChargesAndOther" xlink:href="codi-20241231.xsd#codi_NoncontrollingStockholderChargesAndOther"/>
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    <link:label id="lab_ecd_PvpTableTextBlock_label_en-US" xlink:label="lab_ecd_PvpTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Pay vs Performance [Table Text Block]</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfAllocationOfPlanAssetsTableTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_ScheduleOfAllocationOfPlanAssetsTableTextBlock"/>
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    <link:label id="lab_dei_EntityFileNumber_label_en-US" xlink:label="lab_dei_EntityFileNumber" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Entity File Number</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityFileNumber" xlink:href="https://xbrl.sec.gov/dei/2024/dei-2024.xsd#dei_EntityFileNumber"/>
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    <link:label id="lab_us-gaap_ScheduleOfAssumptionsUsedTableTextBlock_38d3fb85-5ce6-4cac-9298-25216ec1585f_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfAssumptionsUsedTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Summary of Assumptions Used to Determine the Benefit Obligations and Components of the Net Periodic Benefit Cost</link:label>
    <link:label id="lab_us-gaap_ScheduleOfAssumptionsUsedTableTextBlock_label_en-US" xlink:label="lab_us-gaap_ScheduleOfAssumptionsUsedTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Defined Benefit Plan, Assumptions [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfAssumptionsUsedTableTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_ScheduleOfAssumptionsUsedTableTextBlock"/>
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    <link:label id="lab_srt_ConsolidatedEntitiesDomain_826210d0-f4dd-43e7-9aaa-21426a87c52c_terseLabel_en-US" xlink:label="lab_srt_ConsolidatedEntitiesDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Consolidated Entities [Domain]</link:label>
    <link:label id="lab_srt_ConsolidatedEntitiesDomain_label_en-US" xlink:label="lab_srt_ConsolidatedEntitiesDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Consolidated Entities [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_srt_ConsolidatedEntitiesDomain" xlink:href="https://xbrl.fasb.org/srt/2024/elts/srt-2024.xsd#srt_ConsolidatedEntitiesDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_srt_ConsolidatedEntitiesDomain" xlink:to="lab_srt_ConsolidatedEntitiesDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_NoncontrollingInterestMember_4f0ec98d-22a4-4683-8ee6-4bae82c83c0a_terseLabel_en-US" xlink:label="lab_us-gaap_NoncontrollingInterestMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Noncontrolling Interest [Member]</link:label>
    <link:label id="lab_us-gaap_NoncontrollingInterestMember_0faee323-127c-4233-8f0d-944ec45b5489_verboseLabel_en-US" xlink:label="lab_us-gaap_NoncontrollingInterestMember" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Non-Controlling Interest</link:label>
    <link:label id="lab_us-gaap_NoncontrollingInterestMember_label_en-US" xlink:label="lab_us-gaap_NoncontrollingInterestMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Noncontrolling Interest [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_NoncontrollingInterestMember" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_NoncontrollingInterestMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_NoncontrollingInterestMember" xlink:to="lab_us-gaap_NoncontrollingInterestMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_IncomeStatementAbstract_e2e190bd-1cad-45b5-95c2-b60dfce9d707_terseLabel_en-US" xlink:label="lab_us-gaap_IncomeStatementAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Income Statement [Abstract]</link:label>
    <link:label id="lab_us-gaap_IncomeStatementAbstract_label_en-US" xlink:label="lab_us-gaap_IncomeStatementAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Income Statement [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncomeStatementAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_IncomeStatementAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_IncomeStatementAbstract" xlink:to="lab_us-gaap_IncomeStatementAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_EntityAddressAddressLine1_383a5edd-0fc9-4559-9919-229a531a0ad1_terseLabel_en-US" xlink:label="lab_dei_EntityAddressAddressLine1" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Entity Address, Address Line One</link:label>
    <link:label id="lab_dei_EntityAddressAddressLine1_label_en-US" xlink:label="lab_dei_EntityAddressAddressLine1" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Entity Address, Address Line One</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityAddressAddressLine1" xlink:href="https://xbrl.sec.gov/dei/2024/dei-2024.xsd#dei_EntityAddressAddressLine1"/>
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    <link:label id="lab_us-gaap_CapitalLossCarryforwardMember_cc7be6cf-9e9d-4b7a-8787-024efbf4f0c0_terseLabel_en-US" xlink:label="lab_us-gaap_CapitalLossCarryforwardMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Capital Loss Carryforward</link:label>
    <link:label id="lab_us-gaap_CapitalLossCarryforwardMember_label_en-US" xlink:label="lab_us-gaap_CapitalLossCarryforwardMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Capital Loss Carryforward [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CapitalLossCarryforwardMember" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_CapitalLossCarryforwardMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CapitalLossCarryforwardMember" xlink:to="lab_us-gaap_CapitalLossCarryforwardMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CurrentFederalTaxExpenseBenefit_72086d90-3603-419f-a861-5b9d09e636c7_terseLabel_en-US" xlink:label="lab_us-gaap_CurrentFederalTaxExpenseBenefit" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Federal</link:label>
    <link:label id="lab_us-gaap_CurrentFederalTaxExpenseBenefit_label_en-US" xlink:label="lab_us-gaap_CurrentFederalTaxExpenseBenefit" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Current Federal Tax Expense (Benefit)</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CurrentFederalTaxExpenseBenefit" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_CurrentFederalTaxExpenseBenefit"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CurrentFederalTaxExpenseBenefit" xlink:to="lab_us-gaap_CurrentFederalTaxExpenseBenefit" xlink:type="arc" order="1"/>
    <link:label id="lab_codi_GainOnElectionToBeTreatedAsCorporationUSFederalTax_88801d8a-27de-483d-8764-9c5d470a1406_terseLabel_en-US" xlink:label="lab_codi_GainOnElectionToBeTreatedAsCorporationUSFederalTax" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Gain on Election to be treated as Corporation - US Federal Tax</link:label>
    <link:label id="lab_codi_GainOnElectionToBeTreatedAsCorporationUSFederalTax_label_en-US" xlink:label="lab_codi_GainOnElectionToBeTreatedAsCorporationUSFederalTax" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Gain on Election to be treated as Corporation - US Federal Tax</link:label>
    <link:label id="lab_codi_GainOnElectionToBeTreatedAsCorporationUSFederalTax_documentation_en-US" xlink:label="lab_codi_GainOnElectionToBeTreatedAsCorporationUSFederalTax" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Gain on Election to be treated as Corporation - US Federal Tax</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_codi_GainOnElectionToBeTreatedAsCorporationUSFederalTax" xlink:href="codi-20241231.xsd#codi_GainOnElectionToBeTreatedAsCorporationUSFederalTax"/>
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    <link:label id="lab_us-gaap_EffectOfExchangeRateOnCashCashEquivalentsRestrictedCashAndRestrictedCashEquivalents_db1922c2-cbf6-4336-b45c-376dcd647b60_terseLabel_en-US" xlink:label="lab_us-gaap_EffectOfExchangeRateOnCashCashEquivalentsRestrictedCashAndRestrictedCashEquivalents" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Foreign currency impact on cash</link:label>
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    <link:label id="lab_ecd_ForgoneRecoveryIndName_terseLabel_en-US" xlink:label="lab_ecd_ForgoneRecoveryIndName" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Name</link:label>
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    <link:label id="lab_us-gaap_OperatingLeaseWeightedAverageRemainingLeaseTerm1_e81eb1ee-5ece-4bff-b608-c65a6bb755cb_terseLabel_en-US" xlink:label="lab_us-gaap_OperatingLeaseWeightedAverageRemainingLeaseTerm1" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Operating Lease, Weighted Average Remaining Lease Term</link:label>
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    <link:label id="lab_us-gaap_OtherNoncashIncomeExpense_fef2bfb7-24d1-4a87-adcf-d1dbfbfe00c8_negatedLabel_en-US" xlink:label="lab_us-gaap_OtherNoncashIncomeExpense" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:type="resource" xml:lang="en-US">Other</link:label>
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    <link:label id="lab_us-gaap_ScheduleOfExpectedBenefitPaymentsTableTextBlock_035b523f-ee93-4282-bdd8-6ee2dee7e37f_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfExpectedBenefitPaymentsTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Summary of Expected Foreign Plan Benefit Payments</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfExpectedBenefitPaymentsTableTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_ScheduleOfExpectedBenefitPaymentsTableTextBlock"/>
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    <link:label id="lab_us-gaap_EffectiveIncomeTaxRateReconciliationNondeductibleExpenseImpairmentLosses_e4d6b79e-57ca-4b28-8d8a-ffc195968081_terseLabel_en-US" xlink:label="lab_us-gaap_EffectiveIncomeTaxRateReconciliationNondeductibleExpenseImpairmentLosses" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Impairment expense</link:label>
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    <link:label id="lab_us-gaap_BusinessAcquisitionProFormaEarningsPerShareBasic_4a3eea4d-758a-4245-a771-5d7c186840d6_terseLabel_en-US" xlink:label="lab_us-gaap_BusinessAcquisitionProFormaEarningsPerShareBasic" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Business Acquisition, Pro Forma Earnings Per Share, Basic</link:label>
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    <link:label id="lab_us-gaap_UnrecognizedTaxBenefitsDecreasesResultingFromPriorPeriodTaxPositions_cfb52c25-19e7-4ee3-a05b-0664b06c3e43_terseLabel_en-US" xlink:label="lab_us-gaap_UnrecognizedTaxBenefitsDecreasesResultingFromPriorPeriodTaxPositions" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Reductions for prior years&#8217; tax positions</link:label>
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    <link:label id="lab_codi_NoncontrollingInterestTableTextBlock_59236207-9ec6-4d25-b9a4-d0fd40bfe615_terseLabel_en-US" xlink:label="lab_codi_NoncontrollingInterestTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Deconsolidation, Effects of IPO</link:label>
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    <link:label id="lab_us-gaap_PreferredClassAMember_label_en-US" xlink:label="lab_us-gaap_PreferredClassAMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Preferred Class A [Member]</link:label>
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    <link:label id="lab_us-gaap_GoodwillFairValueDisclosure_793711b2-50d5-4e36-9e08-f761ddceb5d5_terseLabel_en-US" xlink:label="lab_us-gaap_GoodwillFairValueDisclosure" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Goodwill, Fair Value Disclosure</link:label>
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    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_GoodwillFairValueDisclosure" xlink:to="lab_us-gaap_GoodwillFairValueDisclosure" xlink:type="arc" order="1"/>
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    <link:label id="lab_us-gaap_DiscontinuedOperationsDisposedOfBySaleMember_7990edbe-b30b-4e62-89f0-b58c9d0e1be8_terseLabel_en-US" xlink:label="lab_us-gaap_DiscontinuedOperationsDisposedOfBySaleMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Discontinued Operations, Disposed of by Sale</link:label>
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    <link:label id="lab_codi_BusinessAcquisitionsDistributionsPayableAllocationAgreementPercentage_4368b360-0c17-45e7-93b2-c75c494845de_terseLabel_en-US" xlink:label="lab_codi_BusinessAcquisitionsDistributionsPayableAllocationAgreementPercentage" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Percentage of allocation agreement</link:label>
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    <link:label id="lab_us-gaap_NetIncomeLossAttributableToNoncontrollingInterest_7375682c-c412-4eff-9dd7-d12ebdf2ca6c_terseLabel_en-US" xlink:label="lab_us-gaap_NetIncomeLossAttributableToNoncontrollingInterest" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Less: Net income attributable to noncontrolling interests</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SubsidiaryOrEquityMethodInvesteeSaleOfStockBySubsidiaryOrEquityInvesteeTable" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_SubsidiaryOrEquityMethodInvesteeSaleOfStockBySubsidiaryOrEquityInvesteeTable"/>
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    <link:label id="lab_us-gaap_AccumulatedOtherComprehensiveIncomeLossNetOfTax_2a599d27-58de-4222-8a57-fa82379af539_terseLabel_en-US" xlink:label="lab_us-gaap_AccumulatedOtherComprehensiveIncomeLossNetOfTax" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Accumulated other comprehensive income (loss)</link:label>
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    <link:label id="lab_codi_LesseeOperatingAndFinancingLeaseLiabilityToBePaidYearFour_b4361003-5e82-48a9-b39f-d0092be50ac0_terseLabel_en-US" xlink:label="lab_codi_LesseeOperatingAndFinancingLeaseLiabilityToBePaidYearFour" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Lessee Operating and Financing Lease, Liability, to be Paid, Year Four</link:label>
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    <link:label id="lab_codi_LesseeOperatingAndFinancingLeaseLiabilityToBePaidYearFour_documentation_en-US" xlink:label="lab_codi_LesseeOperatingAndFinancingLeaseLiabilityToBePaidYearFour" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Lessee Operating and Financing Lease, Liability, to be Paid, Year Four</link:label>
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    <link:label id="lab_ecd_PnsnAdjsSvcCstMember_terseLabel_en-US" xlink:label="lab_ecd_PnsnAdjsSvcCstMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Pension Adjustments Service Cost</link:label>
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    <link:label id="lab_us-gaap_RelatedPartyTransactionsByRelatedPartyAxis_e2f8c3f8-0c94-4d78-b483-875bfc0d9800_terseLabel_en-US" xlink:label="lab_us-gaap_RelatedPartyTransactionsByRelatedPartyAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Related Party [Axis]</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_ecd_StkPrcOrTsrEstimationMethodTextBlock" xlink:href="https://xbrl.sec.gov/ecd/2024/ecd-2024.xsd#ecd_StkPrcOrTsrEstimationMethodTextBlock"/>
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    <link:label id="lab_codi_DistributorRelationsAndOtherMember_documentation_en-US" xlink:label="lab_codi_DistributorRelationsAndOtherMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Distributor relations and other.</link:label>
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    <link:label id="lab_codi_LuganoMember_documentation_en-US" xlink:label="lab_codi_LuganoMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Lugano</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_codi_LuganoMember" xlink:href="codi-20241231.xsd#codi_LuganoMember"/>
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    <link:label id="lab_codi_DisposalGroupIncludingDiscontinuedOperationIntercompanyInterestExpenseExcludedfromIncomeLossfromDiscontinuedOperations_90f57100-c4f3-49c3-a6e8-73078a97d4b9_terseLabel_en-US" xlink:label="lab_codi_DisposalGroupIncludingDiscontinuedOperationIntercompanyInterestExpenseExcludedfromIncomeLossfromDiscontinuedOperations" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Disposal Group, Including Discontinued Operation, Intercompany Interest Expense Excluded from Income (Loss) from Discontinued Operations</link:label>
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    <link:label id="lab_us-gaap_SubsidiarySaleOfStockLineItems_0c8f3b61-97b4-4939-b5ba-3e8be4545e59_terseLabel_en-US" xlink:label="lab_us-gaap_SubsidiarySaleOfStockLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Subsidiary, Sale of Stock [Line Items]</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SubsidiarySaleOfStockLineItems" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_SubsidiarySaleOfStockLineItems"/>
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    <link:label id="lab_codi_PaymentstoAcquireBusinessesNetofCashAcquiredandNetofTransactionsCosts_f0d554ae-6de4-40c0-978e-000d5609b9d3_terseLabel_en-US" xlink:label="lab_codi_PaymentstoAcquireBusinessesNetofCashAcquiredandNetofTransactionsCosts" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Purchase price, net</link:label>
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    <link:label id="lab_us-gaap_NatureOfExpenseAxis_label_en-US" xlink:label="lab_us-gaap_NatureOfExpenseAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Nature of Expense [Axis]</link:label>
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    <link:label id="lab_us-gaap_NumberOfStores_702fde8a-1c4d-4f4d-8866-46f1189e2833_terseLabel_en-US" xlink:label="lab_us-gaap_NumberOfStores" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Number of Stores</link:label>
    <link:label id="lab_us-gaap_NumberOfStores_label_en-US" xlink:label="lab_us-gaap_NumberOfStores" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Number of Stores</link:label>
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    <link:label id="lab_us-gaap_ManagementFeeExpense_label_en-US" xlink:label="lab_us-gaap_ManagementFeeExpense" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Management Fee Expense</link:label>
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    <link:label id="lab_us-gaap_SharesIssued_fe0dd09e-b11b-4eaf-987c-7cebdf1405b9_periodStartLabel_en-US" xlink:label="lab_us-gaap_SharesIssued" xlink:role="http://www.xbrl.org/2003/role/periodStartLabel" xlink:type="resource" xml:lang="en-US">Beginning balance (in shares)</link:label>
    <link:label id="lab_us-gaap_SharesIssued_f632068a-455f-41bc-a025-688d02dcbf36_periodEndLabel_en-US" xlink:label="lab_us-gaap_SharesIssued" xlink:role="http://www.xbrl.org/2003/role/periodEndLabel" xlink:type="resource" xml:lang="en-US">Ending balance (in shares)</link:label>
    <link:label id="lab_us-gaap_SharesIssued_be4a99b7-733f-419c-9e32-5e815f8d5f7c_terseLabel_en-US" xlink:label="lab_us-gaap_SharesIssued" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Shares, Issued</link:label>
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    <link:label id="lab_us-gaap_PrivatePlacementMember_a55b309d-51ac-4fd6-bc99-9b77bfaf4607_terseLabel_en-US" xlink:label="lab_us-gaap_PrivatePlacementMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Private Placement</link:label>
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    <link:label id="lab_us-gaap_FederalFundsEffectiveSwapRateMember_9cef4300-e522-4c88-a1ef-a57b3cd532f1_terseLabel_en-US" xlink:label="lab_us-gaap_FederalFundsEffectiveSwapRateMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Federal Funds Effective Swap Rate</link:label>
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    <link:label id="lab_us-gaap_CorporateAndOtherMember_label_en-US" xlink:label="lab_us-gaap_CorporateAndOtherMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Corporate Segment and Other Operating Segment [Member]</link:label>
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    <link:label id="lab_us-gaap_ProceedsFromLongTermLinesOfCredit_264cbae7-f1d4-4653-98fb-b0f1ce7bfccc_terseLabel_en-US" xlink:label="lab_us-gaap_ProceedsFromLongTermLinesOfCredit" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Borrowings under credit facility</link:label>
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    <link:label id="lab_codi_SupplementalPutAccountingPolicyTextBlock_documentation_en-US" xlink:label="lab_codi_SupplementalPutAccountingPolicyTextBlock" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Supplemental put accounting.</link:label>
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    <link:label id="lab_us-gaap_OtherLiabilitiesCurrent_03c640e4-f239-4cf1-8512-ff94f6e34756_terseLabel_en-US" xlink:label="lab_us-gaap_OtherLiabilitiesCurrent" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Other current liabilities</link:label>
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    <link:label id="lab_us-gaap_UnrecognizedTaxBenefitsThatWouldImpactEffectiveTaxRate_d0bc1a7a-e039-44a4-84a7-9cbb356208e5_terseLabel_en-US" xlink:label="lab_us-gaap_UnrecognizedTaxBenefitsThatWouldImpactEffectiveTaxRate" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Unrecognized tax benefits, if recognized, would affect the Company's effective tax rate</link:label>
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    <link:label id="lab_codi_PaymentsforRepurchaseSubsidiaryStock_68886bc1-ce51-41aa-8a37-6d4dfa95989a_terseLabel_en-US" xlink:label="lab_codi_PaymentsforRepurchaseSubsidiaryStock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Purchase of noncontrolling interest</link:label>
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    <link:label id="lab_codi_DistributionExpensePreferredShareholders_fff54d6b-3d24-4115-a598-33193ec6395a_terseLabel_en-US" xlink:label="lab_codi_DistributionExpensePreferredShareholders" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Less: Distributions paid - Preferred Shares</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_ecd_CompActuallyPaidVsNetIncomeTextBlock" xlink:href="https://xbrl.sec.gov/ecd/2024/ecd-2024.xsd#ecd_CompActuallyPaidVsNetIncomeTextBlock"/>
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    <link:label id="lab_us-gaap_TaxCreditCarryforwardAmount_5cb22dcb-1ed1-4f1d-8036-bd6b02ceb4c9_terseLabel_en-US" xlink:label="lab_us-gaap_TaxCreditCarryforwardAmount" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Tax Credit Carryforward, Amount</link:label>
    <link:label id="lab_us-gaap_TaxCreditCarryforwardAmount_label_en-US" xlink:label="lab_us-gaap_TaxCreditCarryforwardAmount" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Tax Credit Carryforward, Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_TaxCreditCarryforwardAmount" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_TaxCreditCarryforwardAmount"/>
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    <link:label id="lab_us-gaap_DisposalGroupIncludingDiscontinuedOperationOperatingIncomeLoss_35701fb7-2bf8-48fc-8148-455d8c8f8564_terseLabel_en-US" xlink:label="lab_us-gaap_DisposalGroupIncludingDiscontinuedOperationOperatingIncomeLoss" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Operating income</link:label>
    <link:label id="lab_us-gaap_DisposalGroupIncludingDiscontinuedOperationOperatingIncomeLoss_label_en-US" xlink:label="lab_us-gaap_DisposalGroupIncludingDiscontinuedOperationOperatingIncomeLoss" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Disposal Group, Including Discontinued Operation, Operating Income (Loss)</link:label>
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    <link:label id="lab_us-gaap_SelectedQuarterlyFinancialInformationAbstract_c470710d-fa8e-4ec7-8797-9bed18eec62a_terseLabel_en-US" xlink:label="lab_us-gaap_SelectedQuarterlyFinancialInformationAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Selected Quarterly Financial Information [Abstract]</link:label>
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    <link:label id="lab_codi_LesseeOperatingAndFinancingLeaseLiabilityToBePaidAfterYearFive_54c2d790-c2ab-43de-ab7c-a64f88a976ec_terseLabel_en-US" xlink:label="lab_codi_LesseeOperatingAndFinancingLeaseLiabilityToBePaidAfterYearFive" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Lessee Operating and Financing Lease, Liability, to be Paid, After Year Five</link:label>
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    <link:label id="lab_codi_BoaMember_documentation_en-US" xlink:label="lab_codi_BoaMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Boa</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_codi_BoaMember" xlink:href="codi-20241231.xsd#codi_BoaMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_codi_BoaMember" xlink:to="lab_codi_BoaMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OtherCommitmentsLineItems_425c7121-8b41-4e85-a94f-d77e14a8762f_terseLabel_en-US" xlink:label="lab_us-gaap_OtherCommitmentsLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Other Commitments [Line Items]</link:label>
    <link:label id="lab_us-gaap_OtherCommitmentsLineItems_label_en-US" xlink:label="lab_us-gaap_OtherCommitmentsLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Other Commitments [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OtherCommitmentsLineItems" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_OtherCommitmentsLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OtherCommitmentsLineItems" xlink:to="lab_us-gaap_OtherCommitmentsLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_GoodwillPurchaseAccountingAdjustments_16662c63-309a-4be5-b7f6-523609c5fd53_terseLabel_en-US" xlink:label="lab_us-gaap_GoodwillPurchaseAccountingAdjustments" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Goodwill, Measurement Period Adjustment</link:label>
    <link:label id="lab_us-gaap_GoodwillPurchaseAccountingAdjustments_label_en-US" xlink:label="lab_us-gaap_GoodwillPurchaseAccountingAdjustments" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Goodwill, Measurement Period Adjustment</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_GoodwillPurchaseAccountingAdjustments" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_GoodwillPurchaseAccountingAdjustments"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_GoodwillPurchaseAccountingAdjustments" xlink:to="lab_us-gaap_GoodwillPurchaseAccountingAdjustments" xlink:type="arc" order="1"/>
    <link:label id="lab_codi_ManagementFeeWaiver_f3d39695-7a0f-4f1b-b0f5-cdcc729e0527_terseLabel_en-US" xlink:label="lab_codi_ManagementFeeWaiver" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Management fee waiver</link:label>
    <link:label id="lab_codi_ManagementFeeWaiver_label_en-US" xlink:label="lab_codi_ManagementFeeWaiver" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Management fee waiver</link:label>
    <link:label id="lab_codi_ManagementFeeWaiver_documentation_en-US" xlink:label="lab_codi_ManagementFeeWaiver" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Management fee waiver</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_codi_ManagementFeeWaiver" xlink:href="codi-20241231.xsd#codi_ManagementFeeWaiver"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_codi_ManagementFeeWaiver" xlink:to="lab_codi_ManagementFeeWaiver" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_EquityMethodInvestments_4b475351-45cc-4275-b11f-2b61b249b32d_terseLabel_en-US" xlink:label="lab_us-gaap_EquityMethodInvestments" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Equity Method Investments</link:label>
    <link:label id="lab_us-gaap_EquityMethodInvestments_label_en-US" xlink:label="lab_us-gaap_EquityMethodInvestments" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Equity Method Investments</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_EquityMethodInvestments" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_EquityMethodInvestments"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_EquityMethodInvestments" xlink:to="lab_us-gaap_EquityMethodInvestments" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_PayVsPerformanceDisclosureLineItems_label_en-US" xlink:label="lab_ecd_PayVsPerformanceDisclosureLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Pay vs Performance Disclosure [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_PayVsPerformanceDisclosureLineItems" xlink:href="https://xbrl.sec.gov/ecd/2024/ecd-2024.xsd#ecd_PayVsPerformanceDisclosureLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_PayVsPerformanceDisclosureLineItems" xlink:to="lab_ecd_PayVsPerformanceDisclosureLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_codi_OwnershipPercentageOfNoncontrollingShareholders_7aa92003-8835-4f9c-993d-a4aa4ea79fc2_terseLabel_en-US" xlink:label="lab_codi_OwnershipPercentageOfNoncontrollingShareholders" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">% Ownership</link:label>
    <link:label id="lab_codi_OwnershipPercentageOfNoncontrollingShareholders_label_en-US" xlink:label="lab_codi_OwnershipPercentageOfNoncontrollingShareholders" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Ownership Percentage Of Noncontrolling Shareholders</link:label>
    <link:label id="lab_codi_OwnershipPercentageOfNoncontrollingShareholders_documentation_en-US" xlink:label="lab_codi_OwnershipPercentageOfNoncontrollingShareholders" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Ownership percentage of noncontrolling shareholders.</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_codi_OwnershipPercentageOfNoncontrollingShareholders" xlink:href="codi-20241231.xsd#codi_OwnershipPercentageOfNoncontrollingShareholders"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_codi_OwnershipPercentageOfNoncontrollingShareholders" xlink:to="lab_codi_OwnershipPercentageOfNoncontrollingShareholders" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_PeerGroupTotalShareholderRtnAmt_terseLabel_en-US" xlink:label="lab_ecd_PeerGroupTotalShareholderRtnAmt" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Peer Group Total Shareholder Return Amount</link:label>
    <link:label id="lab_ecd_PeerGroupTotalShareholderRtnAmt_label_en-US" xlink:label="lab_ecd_PeerGroupTotalShareholderRtnAmt" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Peer Group Total Shareholder Return Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_PeerGroupTotalShareholderRtnAmt" xlink:href="https://xbrl.sec.gov/ecd/2024/ecd-2024.xsd#ecd_PeerGroupTotalShareholderRtnAmt"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_PeerGroupTotalShareholderRtnAmt" xlink:to="lab_ecd_PeerGroupTotalShareholderRtnAmt" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DerivativeTable_afbb993f-dfa4-4906-b149-0d8cdde1c768_terseLabel_en-US" xlink:label="lab_us-gaap_DerivativeTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Derivative [Table]</link:label>
    <link:label id="lab_us-gaap_DerivativeTable_label_en-US" xlink:label="lab_us-gaap_DerivativeTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Derivative [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DerivativeTable" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_DerivativeTable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DerivativeTable" xlink:to="lab_us-gaap_DerivativeTable" xlink:type="arc" order="1"/>
    <link:label id="lab_codi_DistributionsPayableAmountPerShare_064638b9-f75c-4ac2-b020-4e4b3b5e1021_terseLabel_en-US" xlink:label="lab_codi_DistributionsPayableAmountPerShare" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Distribution declared per share (in dollars per share)</link:label>
    <link:label id="lab_codi_DistributionsPayableAmountPerShare_label_en-US" xlink:label="lab_codi_DistributionsPayableAmountPerShare" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Distributions Payable Amount Per Share</link:label>
    <link:label id="lab_codi_DistributionsPayableAmountPerShare_documentation_en-US" xlink:label="lab_codi_DistributionsPayableAmountPerShare" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Distributions payable amount per share.</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_codi_DistributionsPayableAmountPerShare" xlink:href="codi-20241231.xsd#codi_DistributionsPayableAmountPerShare"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_codi_DistributionsPayableAmountPerShare" xlink:to="lab_codi_DistributionsPayableAmountPerShare" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DeferredIncomeTaxExpenseBenefitContinuingOperationsAbstract_6b93646d-4bb1-43fa-88db-1a07bd90f309_terseLabel_en-US" xlink:label="lab_us-gaap_DeferredIncomeTaxExpenseBenefitContinuingOperationsAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Deferred taxes:</link:label>
    <link:label id="lab_us-gaap_DeferredIncomeTaxExpenseBenefitContinuingOperationsAbstract_label_en-US" xlink:label="lab_us-gaap_DeferredIncomeTaxExpenseBenefitContinuingOperationsAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Deferred Income Tax Expense (Benefit), Continuing Operations [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DeferredIncomeTaxExpenseBenefitContinuingOperationsAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_DeferredIncomeTaxExpenseBenefitContinuingOperationsAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DeferredIncomeTaxExpenseBenefitContinuingOperationsAbstract" xlink:to="lab_us-gaap_DeferredIncomeTaxExpenseBenefitContinuingOperationsAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ProceedsFromIssuanceOfPreferredStockAndPreferenceStock_0f6a79bb-627d-4e34-991c-906b7f1484f8_terseLabel_en-US" xlink:label="lab_us-gaap_ProceedsFromIssuanceOfPreferredStockAndPreferenceStock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Proceeds from issuance of preferred stock</link:label>
    <link:label id="lab_us-gaap_ProceedsFromIssuanceOfPreferredStockAndPreferenceStock_label_en-US" xlink:label="lab_us-gaap_ProceedsFromIssuanceOfPreferredStockAndPreferenceStock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Proceeds from Issuance of Preferred Stock and Preference Stock</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ProceedsFromIssuanceOfPreferredStockAndPreferenceStock" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_ProceedsFromIssuanceOfPreferredStockAndPreferenceStock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ProceedsFromIssuanceOfPreferredStockAndPreferenceStock" xlink:to="lab_us-gaap_ProceedsFromIssuanceOfPreferredStockAndPreferenceStock" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_OtherPerfMeasureAmt_terseLabel_en-US" xlink:label="lab_ecd_OtherPerfMeasureAmt" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Other Performance Measure, Amount</link:label>
    <link:label id="lab_ecd_OtherPerfMeasureAmt_label_en-US" xlink:label="lab_ecd_OtherPerfMeasureAmt" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Other Performance Measure, Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_OtherPerfMeasureAmt" xlink:href="https://xbrl.sec.gov/ecd/2024/ecd-2024.xsd#ecd_OtherPerfMeasureAmt"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_OtherPerfMeasureAmt" xlink:to="lab_ecd_OtherPerfMeasureAmt" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseYearThree_844f322d-48e2-4617-8db3-9da8219665b5_terseLabel_en-US" xlink:label="lab_us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseYearThree" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">2022</link:label>
    <link:label id="lab_us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseYearThree_label_en-US" xlink:label="lab_us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseYearThree" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Finite-Lived Intangible Asset, Expected Amortization, Year Three</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseYearThree" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseYearThree"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseYearThree" xlink:to="lab_us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseYearThree" xlink:type="arc" order="1"/>
    <link:label id="lab_codi_NumberOfManufacturingFacilities_16424b58-682b-4a6f-a4c1-ab656d3fb424_terseLabel_en-US" xlink:label="lab_codi_NumberOfManufacturingFacilities" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Number of facilities</link:label>
    <link:label id="lab_codi_NumberOfManufacturingFacilities_label_en-US" xlink:label="lab_codi_NumberOfManufacturingFacilities" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Number Of Manufacturing Facilities</link:label>
    <link:label id="lab_codi_NumberOfManufacturingFacilities_documentation_en-US" xlink:label="lab_codi_NumberOfManufacturingFacilities" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Number of manufacturing facilities.</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_codi_NumberOfManufacturingFacilities" xlink:href="codi-20241231.xsd#codi_NumberOfManufacturingFacilities"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_codi_NumberOfManufacturingFacilities" xlink:to="lab_codi_NumberOfManufacturingFacilities" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DiscontinuedOperationGainLossFromDisposalOfDiscontinuedOperationBeforeIncomeTax_a0b1e16f-89e4-44f1-9932-6316fbefe91c_terseLabel_en-US" xlink:label="lab_us-gaap_DiscontinuedOperationGainLossFromDisposalOfDiscontinuedOperationBeforeIncomeTax" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Discontinued Operation, Gain (Loss) from Disposal of Discontinued Operation, before Income Tax</link:label>
    <link:label id="lab_us-gaap_DiscontinuedOperationGainLossFromDisposalOfDiscontinuedOperationBeforeIncomeTax_label_en-US" xlink:label="lab_us-gaap_DiscontinuedOperationGainLossFromDisposalOfDiscontinuedOperationBeforeIncomeTax" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Discontinued Operation, Gain (Loss) from Disposal of Discontinued Operation, before Income Tax</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DiscontinuedOperationGainLossFromDisposalOfDiscontinuedOperationBeforeIncomeTax" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_DiscontinuedOperationGainLossFromDisposalOfDiscontinuedOperationBeforeIncomeTax"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DiscontinuedOperationGainLossFromDisposalOfDiscontinuedOperationBeforeIncomeTax" xlink:to="lab_us-gaap_DiscontinuedOperationGainLossFromDisposalOfDiscontinuedOperationBeforeIncomeTax" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_GoodwillLineItems_36208df5-4a07-4992-aec0-baced1678b89_terseLabel_en-US" xlink:label="lab_us-gaap_GoodwillLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Goodwill [Line Items]</link:label>
    <link:label id="lab_us-gaap_GoodwillLineItems_label_en-US" xlink:label="lab_us-gaap_GoodwillLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Goodwill [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_GoodwillLineItems" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_GoodwillLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_GoodwillLineItems" xlink:to="lab_us-gaap_GoodwillLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CommonStockSharesOutstanding_db772a75-f618-4541-b3e6-35fa1fda4251_terseLabel_en-US" xlink:label="lab_us-gaap_CommonStockSharesOutstanding" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Trust shares, outstanding (in shares)</link:label>
    <link:label id="lab_us-gaap_CommonStockSharesOutstanding_label_en-US" xlink:label="lab_us-gaap_CommonStockSharesOutstanding" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Common Stock, Shares, Outstanding</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CommonStockSharesOutstanding" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_CommonStockSharesOutstanding"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CommonStockSharesOutstanding" xlink:to="lab_us-gaap_CommonStockSharesOutstanding" xlink:type="arc" order="1"/>
    <link:label id="lab_codi_DefinedBenefitPlanExpectedFutureBenefitPayments_58465603-f62d-4fa4-9c7a-9041e854e93b_totalLabel_en-US" xlink:label="lab_codi_DefinedBenefitPlanExpectedFutureBenefitPayments" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Total</link:label>
    <link:label id="lab_codi_DefinedBenefitPlanExpectedFutureBenefitPayments_label_en-US" xlink:label="lab_codi_DefinedBenefitPlanExpectedFutureBenefitPayments" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Defined Benefit Plan Expected Future Benefit Payments</link:label>
    <link:label id="lab_codi_DefinedBenefitPlanExpectedFutureBenefitPayments_documentation_en-US" xlink:label="lab_codi_DefinedBenefitPlanExpectedFutureBenefitPayments" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Defined benefit plan expected future benefit payments.</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_codi_DefinedBenefitPlanExpectedFutureBenefitPayments" xlink:href="codi-20241231.xsd#codi_DefinedBenefitPlanExpectedFutureBenefitPayments"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_codi_DefinedBenefitPlanExpectedFutureBenefitPayments" xlink:to="lab_codi_DefinedBenefitPlanExpectedFutureBenefitPayments" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ScheduleOfAcquiredFiniteLivedIntangibleAssetByMajorClassTable_ce3649ad-02db-40db-8789-c35e40c53238_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfAcquiredFiniteLivedIntangibleAssetByMajorClassTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Acquired Finite-Lived Intangible Asset by Major Class [Table]</link:label>
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    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_SellingGeneralAndAdministrativeExpensesMember" xlink:to="lab_us-gaap_SellingGeneralAndAdministrativeExpensesMember" xlink:type="arc" order="1"/>
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    <link:label id="lab_us-gaap_TreasuryStockCommonMember_label_en-US" xlink:label="lab_us-gaap_TreasuryStockCommonMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Treasury Stock, Common [Member]</link:label>
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    <link:label id="lab_codi_DeferredTaxAssetsValuationAllowanceInterestCarryforward_documentation_en-US" xlink:label="lab_codi_DeferredTaxAssetsValuationAllowanceInterestCarryforward" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Deferred Tax Assets, Valuation Allowance, Interest Carryforward</link:label>
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    <link:label id="lab_us-gaap_DeferredTaxAssetsNetAbstract_label_en-US" xlink:label="lab_us-gaap_DeferredTaxAssetsNetAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Deferred Tax Assets, Net [Abstract]</link:label>
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    <link:label id="lab_us-gaap_OtherCostAndExpenseOperating_7bc17275-3305-4fad-8da5-626bae761ba3_terseLabel_en-US" xlink:label="lab_us-gaap_OtherCostAndExpenseOperating" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Other Cost and Expense, Operating</link:label>
    <link:label id="lab_us-gaap_OtherCostAndExpenseOperating_label_en-US" xlink:label="lab_us-gaap_OtherCostAndExpenseOperating" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Other Cost and Expense, Operating</link:label>
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    <link:label id="lab_us-gaap_DisposalGroupIncludingDiscontinuedOperationOtherNoncurrentAssets_b1485dbb-76bf-4fd8-93a5-dc8bebbf797b_terseLabel_en-US" xlink:label="lab_us-gaap_DisposalGroupIncludingDiscontinuedOperationOtherNoncurrentAssets" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Disposal Group, Including Discontinued Operation, Other Assets, Noncurrent</link:label>
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    <link:label id="lab_us-gaap_FinanceLeaseLiabilityPaymentsDueAfterYearFive_da4c3345-2600-44e8-b4eb-dcc34abbfe6c_terseLabel_en-US" xlink:label="lab_us-gaap_FinanceLeaseLiabilityPaymentsDueAfterYearFive" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Finance Lease, Liability, to be Paid, after Year Five</link:label>
    <link:label id="lab_us-gaap_FinanceLeaseLiabilityPaymentsDueAfterYearFive_label_en-US" xlink:label="lab_us-gaap_FinanceLeaseLiabilityPaymentsDueAfterYearFive" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Finance Lease, Liability, to be Paid, after Year Five</link:label>
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    <link:label id="lab_us-gaap_FinanceLeaseLiabilityPaymentsDue_label_en-US" xlink:label="lab_us-gaap_FinanceLeaseLiabilityPaymentsDue" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Finance Lease, Liability, to be Paid</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FinanceLeaseLiabilityPaymentsDue" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_FinanceLeaseLiabilityPaymentsDue"/>
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    <link:label id="lab_codi_BusinessCombinationProvisionalInformationInitialAccountingIncompleteAdjustmentCash_0fc5c275-5c90-4f40-80ec-9c6882989c09_terseLabel_en-US" xlink:label="lab_codi_BusinessCombinationProvisionalInformationInitialAccountingIncompleteAdjustmentCash" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Business Combination, Provisional Information, Initial Accounting Incomplete, Adjustment, Cash</link:label>
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    <link:label id="lab_us-gaap_ResearchAndDevelopmentExpensePolicy_48b730d9-e2b8-47b4-8312-b15a5eff830e_terseLabel_en-US" xlink:label="lab_us-gaap_ResearchAndDevelopmentExpensePolicy" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Research and Development</link:label>
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    <link:label id="lab_us-gaap_TradeNamesMember_91436ef4-a0e6-4488-baf7-254575ab587c_terseLabel_en-US" xlink:label="lab_us-gaap_TradeNamesMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Trade name</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_EarningsPerShareDilutedAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_EarningsPerShareDilutedAbstract"/>
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    <link:label id="lab_srt_StatementGeographicalAxis_04e00975-c28a-430c-8f5b-f36f0580d232_terseLabel_en-US" xlink:label="lab_srt_StatementGeographicalAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Geographical [Axis]</link:label>
    <link:label id="lab_srt_StatementGeographicalAxis_label_en-US" xlink:label="lab_srt_StatementGeographicalAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Geographical [Axis]</link:label>
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    <link:label id="lab_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearFive_1c09385c-4743-43ef-be0d-7e884fab0c13_terseLabel_en-US" xlink:label="lab_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearFive" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">2024</link:label>
    <link:label id="lab_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearFive_label_en-US" xlink:label="lab_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearFive" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Lessee, Operating Lease, Liability, to be Paid, Year Five</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearFive" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearFive"/>
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    <link:label id="lab_us-gaap_AccumulatedAmortizationOfNoncurrentDeferredFinanceCosts_label_en-US" xlink:label="lab_us-gaap_AccumulatedAmortizationOfNoncurrentDeferredFinanceCosts" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Accumulated Amortization, Debt Issuance Costs, Noncurrent</link:label>
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    <link:label id="lab_us-gaap_BusinessCombinationConsiderationTransferredAbstract_28c29c0e-1fd9-414f-9bf7-d74be50cda79_terseLabel_en-US" xlink:label="lab_us-gaap_BusinessCombinationConsiderationTransferredAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Acquisition Consideration</link:label>
    <link:label id="lab_us-gaap_BusinessCombinationConsiderationTransferredAbstract_label_en-US" xlink:label="lab_us-gaap_BusinessCombinationConsiderationTransferredAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Business Combination, Consideration Transferred [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_BusinessCombinationConsiderationTransferredAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_BusinessCombinationConsiderationTransferredAbstract"/>
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    <link:label id="lab_codi_LesseeOperatingAndFinancingLeaseLiabilityToBePaidYearThree_0ab5dfb0-3ade-4ca8-bbb5-2b7c19ab203e_terseLabel_en-US" xlink:label="lab_codi_LesseeOperatingAndFinancingLeaseLiabilityToBePaidYearThree" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Lessee Operating and Financing Lease, Liability, to be Paid, Year Three</link:label>
    <link:label id="lab_codi_LesseeOperatingAndFinancingLeaseLiabilityToBePaidYearThree_label_en-US" xlink:label="lab_codi_LesseeOperatingAndFinancingLeaseLiabilityToBePaidYearThree" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Lessee Operating and Financing Lease, Liability, to be Paid, Year Three</link:label>
    <link:label id="lab_codi_LesseeOperatingAndFinancingLeaseLiabilityToBePaidYearThree_documentation_en-US" xlink:label="lab_codi_LesseeOperatingAndFinancingLeaseLiabilityToBePaidYearThree" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Lessee Operating and Financing Lease, Liability, to be Paid, Year Three</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_codi_LesseeOperatingAndFinancingLeaseLiabilityToBePaidYearThree" xlink:href="codi-20241231.xsd#codi_LesseeOperatingAndFinancingLeaseLiabilityToBePaidYearThree"/>
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    <link:label id="lab_us-gaap_StockRepurchasedDuringPeriodValue_8ce430ce-d747-4179-982c-a7df31a20f16_terseLabel_en-US" xlink:label="lab_us-gaap_StockRepurchasedDuringPeriodValue" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Stock Repurchased During Period, Value</link:label>
    <link:label id="lab_us-gaap_StockRepurchasedDuringPeriodValue_label_en-US" xlink:label="lab_us-gaap_StockRepurchasedDuringPeriodValue" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Stock Repurchased During Period, Value</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_StockRepurchasedDuringPeriodValue" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_StockRepurchasedDuringPeriodValue"/>
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    <link:label id="lab_us-gaap_ProceedsFromIssuanceOfOtherLongTermDebt_e3980bc3-c14a-497f-a880-0e92136b6434_terseLabel_en-US" xlink:label="lab_us-gaap_ProceedsFromIssuanceOfOtherLongTermDebt" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Proceeds from Issuance of Other Long-term Debt</link:label>
    <link:label id="lab_us-gaap_ProceedsFromIssuanceOfOtherLongTermDebt_label_en-US" xlink:label="lab_us-gaap_ProceedsFromIssuanceOfOtherLongTermDebt" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Proceeds from Issuance of Other Long-Term Debt</link:label>
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    <link:label id="lab_ecd_EqtyAwrdsInSummryCompstnTblForAplblYrMember_terseLabel_en-US" xlink:label="lab_ecd_EqtyAwrdsInSummryCompstnTblForAplblYrMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Aggregate Grant Date Fair Value of Equity Award Amounts Reported in Summary Compensation Table</link:label>
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    <link:label id="lab_us-gaap_CompensationAndEmployeeBenefitPlansTextBlock_beeb04b1-691b-4a89-b337-f7dba6944534_terseLabel_en-US" xlink:label="lab_us-gaap_CompensationAndEmployeeBenefitPlansTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Compensation and Employee Benefit Plans [Text Block]</link:label>
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    <link:label id="lab_us-gaap_IncomeLossFromDiscontinuedOperationsNetOfTaxAttributableToNoncontrollingInterest_d786d477-44d4-4a26-883b-1afed0e1b0b2_terseLabel_en-US" xlink:label="lab_us-gaap_IncomeLossFromDiscontinuedOperationsNetOfTaxAttributableToNoncontrollingInterest" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Less: Net income (loss) from discontinued operations attributable to noncontrolling interest</link:label>
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    <link:label id="lab_codi_QuarterlyManagementFeePercentageOfEntityAdjustedNetAssets_6b2525bb-42cd-444c-8494-3bde0ef0ac9b_terseLabel_en-US" xlink:label="lab_codi_QuarterlyManagementFeePercentageOfEntityAdjustedNetAssets" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Management fees paid equal to net asset</link:label>
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    <link:label id="lab_us-gaap_CurrentForeignTaxExpenseBenefit_cda85b28-ce27-4274-b700-1f941d09fb60_terseLabel_en-US" xlink:label="lab_us-gaap_CurrentForeignTaxExpenseBenefit" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Foreign</link:label>
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    <link:label id="lab_us-gaap_AssetsCurrentAbstract_531c4db3-b6b2-43b5-a1f0-3873a96c7273_terseLabel_en-US" xlink:label="lab_us-gaap_AssetsCurrentAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Current assets:</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IndefiniteLivedIntangibleAssetsMajorClassNameDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_IndefiniteLivedIntangibleAssetsMajorClassNameDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_IndefiniteLivedIntangibleAssetsMajorClassNameDomain" xlink:to="lab_us-gaap_IndefiniteLivedIntangibleAssetsMajorClassNameDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FairValueOfFinancialInstrumentsPolicy_36342406-5185-4dd1-99ee-6b4562cd1781_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueOfFinancialInstrumentsPolicy" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Fair Value of Financial Instruments</link:label>
    <link:label id="lab_us-gaap_FairValueOfFinancialInstrumentsPolicy_label_en-US" xlink:label="lab_us-gaap_FairValueOfFinancialInstrumentsPolicy" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fair Value of Financial Instruments, Policy [Policy Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueOfFinancialInstrumentsPolicy" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_FairValueOfFinancialInstrumentsPolicy"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FairValueOfFinancialInstrumentsPolicy" xlink:to="lab_us-gaap_FairValueOfFinancialInstrumentsPolicy" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_IncomeLossFromContinuingOperations_90167167-863a-4d48-b5af-5b98cfc1f670_terseLabel_en-US" xlink:label="lab_us-gaap_IncomeLossFromContinuingOperations" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Income (loss) from continuing operations</link:label>
    <link:label id="lab_us-gaap_IncomeLossFromContinuingOperations_label_en-US" xlink:label="lab_us-gaap_IncomeLossFromContinuingOperations" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Income (Loss) from Continuing Operations, Net of Tax, Attributable to Parent</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncomeLossFromContinuingOperations" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_IncomeLossFromContinuingOperations"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_IncomeLossFromContinuingOperations" xlink:to="lab_us-gaap_IncomeLossFromContinuingOperations" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_ForgoneRecoveryDueToDisqualificationOfTaxBenefitsAmt_terseLabel_en-US" xlink:label="lab_ecd_ForgoneRecoveryDueToDisqualificationOfTaxBenefitsAmt" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Forgone Recovery due to Disqualification of Tax Benefits, Amount</link:label>
    <link:label id="lab_ecd_ForgoneRecoveryDueToDisqualificationOfTaxBenefitsAmt_label_en-US" xlink:label="lab_ecd_ForgoneRecoveryDueToDisqualificationOfTaxBenefitsAmt" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Forgone Recovery due to Disqualification of Tax Benefits, Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_ForgoneRecoveryDueToDisqualificationOfTaxBenefitsAmt" xlink:href="https://xbrl.sec.gov/ecd/2024/ecd-2024.xsd#ecd_ForgoneRecoveryDueToDisqualificationOfTaxBenefitsAmt"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_ForgoneRecoveryDueToDisqualificationOfTaxBenefitsAmt" xlink:to="lab_ecd_ForgoneRecoveryDueToDisqualificationOfTaxBenefitsAmt" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_InterestPaid_28b0f213-0e63-431a-8086-2e38d7849862_terseLabel_en-US" xlink:label="lab_us-gaap_InterestPaid" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Interest paid</link:label>
    <link:label id="lab_us-gaap_InterestPaid_label_en-US" xlink:label="lab_us-gaap_InterestPaid" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Interest Paid, Including Capitalized Interest, Operating and Investing Activities</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_InterestPaid" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_InterestPaid"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_InterestPaid" xlink:to="lab_us-gaap_InterestPaid" xlink:type="arc" order="1"/>
    <link:label id="lab_srt_ProductsAndServicesDomain_9bcc045b-cf91-48bf-8f8c-8557b39cb2d7_terseLabel_en-US" xlink:label="lab_srt_ProductsAndServicesDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Product and Service [Domain]</link:label>
    <link:label id="lab_srt_ProductsAndServicesDomain_label_en-US" xlink:label="lab_srt_ProductsAndServicesDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Product and Service [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_srt_ProductsAndServicesDomain" xlink:href="https://xbrl.fasb.org/srt/2024/elts/srt-2024.xsd#srt_ProductsAndServicesDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_srt_ProductsAndServicesDomain" xlink:to="lab_srt_ProductsAndServicesDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AllowanceForCreditLossMember_fb6a500c-ad00-40ac-bcb8-be381e5f806d_terseLabel_en-US" xlink:label="lab_us-gaap_AllowanceForCreditLossMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Allowance for Doubtful Accounts</link:label>
    <link:label id="lab_us-gaap_AllowanceForCreditLossMember_label_en-US" xlink:label="lab_us-gaap_AllowanceForCreditLossMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">SEC Schedule, 12-09, Allowance, Credit Loss [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AllowanceForCreditLossMember" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_AllowanceForCreditLossMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AllowanceForCreditLossMember" xlink:to="lab_us-gaap_AllowanceForCreditLossMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_GoodwillRollForward_eed511a2-1556-407f-a502-8ba4a01bbbc2_terseLabel_en-US" xlink:label="lab_us-gaap_GoodwillRollForward" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Goodwill [Roll Forward]</link:label>
    <link:label id="lab_us-gaap_GoodwillRollForward_label_en-US" xlink:label="lab_us-gaap_GoodwillRollForward" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Goodwill [Roll Forward]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_GoodwillRollForward" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_GoodwillRollForward"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_GoodwillRollForward" xlink:to="lab_us-gaap_GoodwillRollForward" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FairValueDisclosuresAbstract_7e892de0-bc3e-4e31-8346-8b0de20cee7b_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueDisclosuresAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Fair Value Disclosures [Abstract]</link:label>
    <link:label id="lab_us-gaap_FairValueDisclosuresAbstract_label_en-US" xlink:label="lab_us-gaap_FairValueDisclosuresAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fair Value Disclosures [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueDisclosuresAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_FairValueDisclosuresAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FairValueDisclosuresAbstract" xlink:to="lab_us-gaap_FairValueDisclosuresAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_codi_MarucciMember_c3c57c50-1f2e-4a2e-a3b9-b8624afd80b8_terseLabel_en-US" xlink:label="lab_codi_MarucciMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Marucci</link:label>
    <link:label id="lab_codi_MarucciMember_label_en-US" xlink:label="lab_codi_MarucciMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Marucci [Member]</link:label>
    <link:label id="lab_codi_MarucciMember_documentation_en-US" xlink:label="lab_codi_MarucciMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Marucci</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_codi_MarucciMember" xlink:href="codi-20241231.xsd#codi_MarucciMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_codi_MarucciMember" xlink:to="lab_codi_MarucciMember" xlink:type="arc" order="1"/>
    <link:label id="lab_codi_FairValueAssetsLiabilitiesQuantitativeInformationLineItems_d9d53175-bce9-4f22-9942-17e9af4c388d_terseLabel_en-US" xlink:label="lab_codi_FairValueAssetsLiabilitiesQuantitativeInformationLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Fair Value Assets Liabilities Quantitative Information [Line Items]</link:label>
    <link:label id="lab_codi_FairValueAssetsLiabilitiesQuantitativeInformationLineItems_label_en-US" xlink:label="lab_codi_FairValueAssetsLiabilitiesQuantitativeInformationLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fair Value Assets Liabilities Quantitative Information [Line Items]</link:label>
    <link:label id="lab_codi_FairValueAssetsLiabilitiesQuantitativeInformationLineItems_documentation_en-US" xlink:label="lab_codi_FairValueAssetsLiabilitiesQuantitativeInformationLineItems" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Fair Value Assets Liabilities Quantitative Information [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_codi_FairValueAssetsLiabilitiesQuantitativeInformationLineItems" xlink:href="codi-20241231.xsd#codi_FairValueAssetsLiabilitiesQuantitativeInformationLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_codi_FairValueAssetsLiabilitiesQuantitativeInformationLineItems" xlink:to="lab_codi_FairValueAssetsLiabilitiesQuantitativeInformationLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_StandardProductWarrantyAccrualPayments_f1170976-6924-4261-a53c-5408b3799ce2_negatedLabel_en-US" xlink:label="lab_us-gaap_StandardProductWarrantyAccrualPayments" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:type="resource" xml:lang="en-US">Warranty payments</link:label>
    <link:label id="lab_us-gaap_StandardProductWarrantyAccrualPayments_label_en-US" xlink:label="lab_us-gaap_StandardProductWarrantyAccrualPayments" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Standard Product Warranty Accrual, Decrease for Payments</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_StandardProductWarrantyAccrualPayments" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_StandardProductWarrantyAccrualPayments"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_StandardProductWarrantyAccrualPayments" xlink:to="lab_us-gaap_StandardProductWarrantyAccrualPayments" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_PreferredStockSharesOutstanding_257cbfa3-9550-456a-90dc-c09d5e6aea2a_terseLabel_en-US" xlink:label="lab_us-gaap_PreferredStockSharesOutstanding" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Preferred Stock, Shares Outstanding</link:label>
    <link:label id="lab_us-gaap_PreferredStockSharesOutstanding_label_en-US" xlink:label="lab_us-gaap_PreferredStockSharesOutstanding" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Preferred Stock, Shares Outstanding</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PreferredStockSharesOutstanding" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_PreferredStockSharesOutstanding"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PreferredStockSharesOutstanding" xlink:to="lab_us-gaap_PreferredStockSharesOutstanding" xlink:type="arc" order="1"/>
    <link:label id="lab_codi_PreferredSharesRedemptionFundamentalChangeNoticePeriod_bc0cbf78-8e4d-4676-a242-450b8c198b21_terseLabel_en-US" xlink:label="lab_codi_PreferredSharesRedemptionFundamentalChangeNoticePeriod" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Preferred Shares Redemption, Fundamental Change, Notice Period</link:label>
    <link:label id="lab_codi_PreferredSharesRedemptionFundamentalChangeNoticePeriod_label_en-US" xlink:label="lab_codi_PreferredSharesRedemptionFundamentalChangeNoticePeriod" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Preferred Shares Redemption, Fundamental Change, Notice Period</link:label>
    <link:label id="lab_codi_PreferredSharesRedemptionFundamentalChangeNoticePeriod_documentation_en-US" xlink:label="lab_codi_PreferredSharesRedemptionFundamentalChangeNoticePeriod" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Preferred Shares Redemption, Fundamental Change, Notice Period</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_codi_PreferredSharesRedemptionFundamentalChangeNoticePeriod" xlink:href="codi-20241231.xsd#codi_PreferredSharesRedemptionFundamentalChangeNoticePeriod"/>
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    <link:label id="lab_us-gaap_ScheduleOfRevenueFromExternalCustomersAttributedToForeignCountriesByGeographicAreaTextBlock_78a599a8-ae58-451f-8cc1-b644a2280188_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfRevenueFromExternalCustomersAttributedToForeignCountriesByGeographicAreaTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Revenues from Geographic Locations Outside Domestic Country</link:label>
    <link:label id="lab_us-gaap_ScheduleOfRevenueFromExternalCustomersAttributedToForeignCountriesByGeographicAreaTextBlock_label_en-US" xlink:label="lab_us-gaap_ScheduleOfRevenueFromExternalCustomersAttributedToForeignCountriesByGeographicAreaTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Schedule of Revenue from External Customers Attributed to Foreign Countries by Geographic Area [Table Text Block]</link:label>
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    <link:label id="lab_dei_SecurityExchangeName_36e20603-e82e-4245-a8d2-c0342ab4e866_terseLabel_en-US" xlink:label="lab_dei_SecurityExchangeName" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Security Exchange Name</link:label>
    <link:label id="lab_dei_SecurityExchangeName_label_en-US" xlink:label="lab_dei_SecurityExchangeName" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Security Exchange Name</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_SecurityExchangeName" xlink:href="https://xbrl.sec.gov/dei/2024/dei-2024.xsd#dei_SecurityExchangeName"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_SecurityExchangeName" xlink:to="lab_dei_SecurityExchangeName" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_RelatedPartyTransactionDomain_ebd0287f-5aa5-464d-b698-3ea0c06e5843_terseLabel_en-US" xlink:label="lab_us-gaap_RelatedPartyTransactionDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Related Party Transaction [Domain]</link:label>
    <link:label id="lab_us-gaap_RelatedPartyTransactionDomain_label_en-US" xlink:label="lab_us-gaap_RelatedPartyTransactionDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Related Party Transaction [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_RelatedPartyTransactionDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_RelatedPartyTransactionDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_RelatedPartyTransactionDomain" xlink:to="lab_us-gaap_RelatedPartyTransactionDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OtherComprehensiveIncomeLossNetOfTaxPortionAttributableToNoncontrollingInterest_1e42981a-b7c5-4249-afb5-74b1851b4bdd_terseLabel_en-US" xlink:label="lab_us-gaap_OtherComprehensiveIncomeLossNetOfTaxPortionAttributableToNoncontrollingInterest" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Less: Other comprehensive income (loss) attributable to noncontrolling interests</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OtherComprehensiveIncomeLossNetOfTaxPortionAttributableToNoncontrollingInterest" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_OtherComprehensiveIncomeLossNetOfTaxPortionAttributableToNoncontrollingInterest"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OtherComprehensiveIncomeLossNetOfTaxPortionAttributableToNoncontrollingInterest" xlink:to="lab_us-gaap_OtherComprehensiveIncomeLossNetOfTaxPortionAttributableToNoncontrollingInterest" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_EurodollarMember_b289e29a-2b0a-4611-b896-9d6a93588467_terseLabel_en-US" xlink:label="lab_us-gaap_EurodollarMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Eurodollar</link:label>
    <link:label id="lab_us-gaap_EurodollarMember_label_en-US" xlink:label="lab_us-gaap_EurodollarMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Eurodollar [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_EurodollarMember" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_EurodollarMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_EurodollarMember" xlink:to="lab_us-gaap_EurodollarMember" xlink:type="arc" order="1"/>
    <link:label id="lab_codi_EffectOfContributionBasedProfitOnNetIncomeLossBecauseOfHoldingEvent_52cf2d89-7471-42c6-9a88-2b3b1575186d_negatedTerseLabel_en-US" xlink:label="lab_codi_EffectOfContributionBasedProfitOnNetIncomeLossBecauseOfHoldingEvent" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Less: Effect of contribution based profit&#8212;Holding Event</link:label>
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    <link:label id="lab_codi_AdjustedNetAssets_label_en-US" xlink:label="lab_codi_AdjustedNetAssets" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Adjusted Net Assets</link:label>
    <link:label id="lab_codi_AdjustedNetAssets_documentation_en-US" xlink:label="lab_codi_AdjustedNetAssets" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Adjusted Net Assets</link:label>
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    <link:label id="lab_us-gaap_CurrentStateAndLocalTaxExpenseBenefit_644aecb4-0d3e-4458-b609-4a574273c48a_terseLabel_en-US" xlink:label="lab_us-gaap_CurrentStateAndLocalTaxExpenseBenefit" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">State</link:label>
    <link:label id="lab_us-gaap_CurrentStateAndLocalTaxExpenseBenefit_label_en-US" xlink:label="lab_us-gaap_CurrentStateAndLocalTaxExpenseBenefit" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Current State and Local Tax Expense (Benefit)</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CurrentStateAndLocalTaxExpenseBenefit" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_CurrentStateAndLocalTaxExpenseBenefit"/>
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    <link:label id="lab_ecd_ForgoneRecoveryExplanationOfImpracticabilityTextBlock_terseLabel_en-US" xlink:label="lab_ecd_ForgoneRecoveryExplanationOfImpracticabilityTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Forgone Recovery, Explanation of Impracticability</link:label>
    <link:label id="lab_ecd_ForgoneRecoveryExplanationOfImpracticabilityTextBlock_label_en-US" xlink:label="lab_ecd_ForgoneRecoveryExplanationOfImpracticabilityTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Forgone Recovery, Explanation of Impracticability [Text Block]</link:label>
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    <link:label id="lab_us-gaap_ResearchAndDevelopmentExpense_787e230d-600f-4bc2-a7cb-bcbc5ce919c4_terseLabel_en-US" xlink:label="lab_us-gaap_ResearchAndDevelopmentExpense" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Research and development expense</link:label>
    <link:label id="lab_us-gaap_ResearchAndDevelopmentExpense_label_en-US" xlink:label="lab_us-gaap_ResearchAndDevelopmentExpense" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Research and Development Expense</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ResearchAndDevelopmentExpense" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_ResearchAndDevelopmentExpense"/>
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    <link:label id="lab_us-gaap_RightOfUseAssetObtainedInExchangeForFinanceLeaseLiability_351b6951-47e3-4298-bd43-cae57674d0c2_terseLabel_en-US" xlink:label="lab_us-gaap_RightOfUseAssetObtainedInExchangeForFinanceLeaseLiability" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Right-of-Use Asset Obtained in Exchange for Finance Lease Liability</link:label>
    <link:label id="lab_us-gaap_RightOfUseAssetObtainedInExchangeForFinanceLeaseLiability_label_en-US" xlink:label="lab_us-gaap_RightOfUseAssetObtainedInExchangeForFinanceLeaseLiability" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Right-of-Use Asset Obtained in Exchange for Finance Lease Liability</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_RightOfUseAssetObtainedInExchangeForFinanceLeaseLiability" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_RightOfUseAssetObtainedInExchangeForFinanceLeaseLiability"/>
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    <link:label id="lab_us-gaap_FairValueMeasurementsNonrecurringMember_89c6625d-f3cf-444e-9b86-cee469e5a94e_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueMeasurementsNonrecurringMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Fair Value, Measurements, Nonrecurring</link:label>
    <link:label id="lab_us-gaap_FairValueMeasurementsNonrecurringMember_label_en-US" xlink:label="lab_us-gaap_FairValueMeasurementsNonrecurringMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fair Value, Nonrecurring [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueMeasurementsNonrecurringMember" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_FairValueMeasurementsNonrecurringMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FairValueMeasurementsNonrecurringMember" xlink:to="lab_us-gaap_FairValueMeasurementsNonrecurringMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_SubsegmentsAxis_b3f5b3a1-4487-4157-b989-eb132e4fd718_terseLabel_en-US" xlink:label="lab_us-gaap_SubsegmentsAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Subsegments [Axis]</link:label>
    <link:label id="lab_us-gaap_SubsegmentsAxis_label_en-US" xlink:label="lab_us-gaap_SubsegmentsAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Subsegments [Axis]</link:label>
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    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_SubsegmentsAxis" xlink:to="lab_us-gaap_SubsegmentsAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_GoodwillAndIntangibleAssetsDisclosureAbstract_88503dc8-3e9c-4758-898e-e6f17f2e67f6_terseLabel_en-US" xlink:label="lab_us-gaap_GoodwillAndIntangibleAssetsDisclosureAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Goodwill and Intangible Assets Disclosure [Abstract]</link:label>
    <link:label id="lab_us-gaap_GoodwillAndIntangibleAssetsDisclosureAbstract_label_en-US" xlink:label="lab_us-gaap_GoodwillAndIntangibleAssetsDisclosureAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Goodwill and Intangible Assets Disclosure [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_GoodwillAndIntangibleAssetsDisclosureAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_GoodwillAndIntangibleAssetsDisclosureAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_GoodwillAndIntangibleAssetsDisclosureAbstract" xlink:to="lab_us-gaap_GoodwillAndIntangibleAssetsDisclosureAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CommonStockSharesIssued_1afe77ce-4122-4998-b1d9-4512694f3076_terseLabel_en-US" xlink:label="lab_us-gaap_CommonStockSharesIssued" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Trust shares, issued (in shares)</link:label>
    <link:label id="lab_us-gaap_CommonStockSharesIssued_label_en-US" xlink:label="lab_us-gaap_CommonStockSharesIssued" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Common Stock, Shares, Issued</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CommonStockSharesIssued" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_CommonStockSharesIssued"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CommonStockSharesIssued" xlink:to="lab_us-gaap_CommonStockSharesIssued" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_RetirementPlanNameDomain_11fed275-466d-4d44-bfa6-20d41dbb521f_terseLabel_en-US" xlink:label="lab_us-gaap_RetirementPlanNameDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Retirement Plan Name [Domain]</link:label>
    <link:label id="lab_us-gaap_RetirementPlanNameDomain_label_en-US" xlink:label="lab_us-gaap_RetirementPlanNameDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Retirement Plan Name [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_RetirementPlanNameDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_RetirementPlanNameDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_RetirementPlanNameDomain" xlink:to="lab_us-gaap_RetirementPlanNameDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_EntityDomain_1da5bf6e-dbaf-48a5-aa17-dba315819314_terseLabel_en-US" xlink:label="lab_dei_EntityDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Entity [Domain]</link:label>
    <link:label id="lab_dei_EntityDomain_label_en-US" xlink:label="lab_dei_EntityDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Entity [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityDomain" xlink:href="https://xbrl.sec.gov/dei/2024/dei-2024.xsd#dei_EntityDomain"/>
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    <link:label id="lab_us-gaap_LineOfCreditFacilityMaximumBorrowingCapacity_0fd55ad7-11d5-4cab-8f07-1fd4892ed92d_terseLabel_en-US" xlink:label="lab_us-gaap_LineOfCreditFacilityMaximumBorrowingCapacity" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Line of Credit Facility, Maximum Borrowing Capacity</link:label>
    <link:label id="lab_us-gaap_LineOfCreditFacilityMaximumBorrowingCapacity_label_en-US" xlink:label="lab_us-gaap_LineOfCreditFacilityMaximumBorrowingCapacity" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Line of Credit Facility, Maximum Borrowing Capacity</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LineOfCreditFacilityMaximumBorrowingCapacity" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_LineOfCreditFacilityMaximumBorrowingCapacity"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LineOfCreditFacilityMaximumBorrowingCapacity" xlink:to="lab_us-gaap_LineOfCreditFacilityMaximumBorrowingCapacity" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AssetsOfDisposalGroupIncludingDiscontinuedOperation_2800bbe4-c97d-4a2a-813a-1ab729bff909_terseLabel_en-US" xlink:label="lab_us-gaap_AssetsOfDisposalGroupIncludingDiscontinuedOperation" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Disposal Group, Including Discontinued Operation, Assets</link:label>
    <link:label id="lab_us-gaap_AssetsOfDisposalGroupIncludingDiscontinuedOperation_label_en-US" xlink:label="lab_us-gaap_AssetsOfDisposalGroupIncludingDiscontinuedOperation" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Disposal Group, Including Discontinued Operation, Assets</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AssetsOfDisposalGroupIncludingDiscontinuedOperation" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_AssetsOfDisposalGroupIncludingDiscontinuedOperation"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AssetsOfDisposalGroupIncludingDiscontinuedOperation" xlink:to="lab_us-gaap_AssetsOfDisposalGroupIncludingDiscontinuedOperation" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_InsiderTrdPoliciesProcAdoptedFlag_terseLabel_en-US" xlink:label="lab_ecd_InsiderTrdPoliciesProcAdoptedFlag" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Insider Trading Policies and Procedures Adopted</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_ecd_InsiderTrdPoliciesProcAdoptedFlag" xlink:href="https://xbrl.sec.gov/ecd/2024/ecd-2024.xsd#ecd_InsiderTrdPoliciesProcAdoptedFlag"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_InsiderTrdPoliciesProcAdoptedFlag" xlink:to="lab_ecd_InsiderTrdPoliciesProcAdoptedFlag" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AccumulatedDepreciationDepletionAndAmortizationPropertyPlantAndEquipment_a60567f3-acee-4a0a-b220-15324ca16040_negatedLabel_en-US" xlink:label="lab_us-gaap_AccumulatedDepreciationDepletionAndAmortizationPropertyPlantAndEquipment" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:type="resource" xml:lang="en-US">Less: accumulated depreciation</link:label>
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    <link:label id="lab_us-gaap_AccountsReceivableNet_cb6f893f-44bc-4166-8faa-39cb14580ecd_terseLabel_en-US" xlink:label="lab_us-gaap_AccountsReceivableNet" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Accounts Receivable, after Allowance for Credit Loss</link:label>
    <link:label id="lab_us-gaap_AccountsReceivableNet_label_en-US" xlink:label="lab_us-gaap_AccountsReceivableNet" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Accounts Receivable, after Allowance for Credit Loss</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AccountsReceivableNet" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_AccountsReceivableNet"/>
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    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DefinedBenefitPlanRecognizedNetGainLossDueToSettlements1" xlink:to="lab_us-gaap_DefinedBenefitPlanRecognizedNetGainLossDueToSettlements1" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DiscontinuedOperationsPolicyTextBlock_b6243cac-1d91-4438-b6d8-daeb699df619_terseLabel_en-US" xlink:label="lab_us-gaap_DiscontinuedOperationsPolicyTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Discontinued Operations</link:label>
    <link:label id="lab_us-gaap_DiscontinuedOperationsPolicyTextBlock_label_en-US" xlink:label="lab_us-gaap_DiscontinuedOperationsPolicyTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Discontinued Operations, Policy [Policy Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DiscontinuedOperationsPolicyTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_DiscontinuedOperationsPolicyTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DiscontinuedOperationsPolicyTextBlock" xlink:to="lab_us-gaap_DiscontinuedOperationsPolicyTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DebtCurrent_fb0ae937-0007-4537-b726-fb4750458f68_terseLabel_en-US" xlink:label="lab_us-gaap_DebtCurrent" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Debt, Current</link:label>
    <link:label id="lab_us-gaap_DebtCurrent_label_en-US" xlink:label="lab_us-gaap_DebtCurrent" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt, Current</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtCurrent" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_DebtCurrent"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DebtCurrent" xlink:to="lab_us-gaap_DebtCurrent" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FairValueMeasurementsRecurringMember_fdebe644-371b-4243-adf3-c67c837a1524_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueMeasurementsRecurringMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Fair Value Measurements Recurring</link:label>
    <link:label id="lab_us-gaap_FairValueMeasurementsRecurringMember_label_en-US" xlink:label="lab_us-gaap_FairValueMeasurementsRecurringMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fair Value, Recurring [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueMeasurementsRecurringMember" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_FairValueMeasurementsRecurringMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FairValueMeasurementsRecurringMember" xlink:to="lab_us-gaap_FairValueMeasurementsRecurringMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AccountsReceivableNetCurrent_2ccc9d39-93b5-41e6-bf14-5f27fbd6eba0_terseLabel_en-US" xlink:label="lab_us-gaap_AccountsReceivableNetCurrent" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Accounts receivable, net</link:label>
    <link:label id="lab_us-gaap_AccountsReceivableNetCurrent_7f0231b7-fc70-4260-9356-eb1760d00437_verboseLabel_en-US" xlink:label="lab_us-gaap_AccountsReceivableNetCurrent" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Total consolidated net accounts receivable</link:label>
    <link:label id="lab_us-gaap_AccountsReceivableNetCurrent_label_en-US" xlink:label="lab_us-gaap_AccountsReceivableNetCurrent" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Accounts Receivable, after Allowance for Credit Loss, Current</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AccountsReceivableNetCurrent" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_AccountsReceivableNetCurrent"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AccountsReceivableNetCurrent" xlink:to="lab_us-gaap_AccountsReceivableNetCurrent" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_RevenuesFromExternalCustomersAndLongLivedAssetsLineItems_153b8258-546f-4832-b392-0517b4e5257d_terseLabel_en-US" xlink:label="lab_us-gaap_RevenuesFromExternalCustomersAndLongLivedAssetsLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Revenues from External Customers and Long-Lived Assets [Line Items]</link:label>
    <link:label id="lab_us-gaap_RevenuesFromExternalCustomersAndLongLivedAssetsLineItems_label_en-US" xlink:label="lab_us-gaap_RevenuesFromExternalCustomersAndLongLivedAssetsLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Revenues from External Customers and Long-Lived Assets [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_RevenuesFromExternalCustomersAndLongLivedAssetsLineItems" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_RevenuesFromExternalCustomersAndLongLivedAssetsLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_RevenuesFromExternalCustomersAndLongLivedAssetsLineItems" xlink:to="lab_us-gaap_RevenuesFromExternalCustomersAndLongLivedAssetsLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AssetImpairmentCharges_1e9ecf0f-38bf-4747-908a-75b2e15c91ab_terseLabel_en-US" xlink:label="lab_us-gaap_AssetImpairmentCharges" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Impairment expense</link:label>
    <link:label id="lab_us-gaap_AssetImpairmentCharges_1c24cac7-8b34-4a89-a43e-f28146e83594_verboseLabel_en-US" xlink:label="lab_us-gaap_AssetImpairmentCharges" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Impairment Expenses</link:label>
    <link:label id="lab_us-gaap_AssetImpairmentCharges_label_en-US" xlink:label="lab_us-gaap_AssetImpairmentCharges" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Asset Impairment Charges</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AssetImpairmentCharges" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_AssetImpairmentCharges"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AssetImpairmentCharges" xlink:to="lab_us-gaap_AssetImpairmentCharges" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LongTermDebt_e029afed-8b69-4aca-aa25-2f28b3782cef_terseLabel_en-US" xlink:label="lab_us-gaap_LongTermDebt" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Total debt</link:label>
    <link:label id="lab_us-gaap_LongTermDebt_label_en-US" xlink:label="lab_us-gaap_LongTermDebt" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Long-Term Debt</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LongTermDebt" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_LongTermDebt"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LongTermDebt" xlink:to="lab_us-gaap_LongTermDebt" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_PnsnAdjsPrrSvcCstMember_terseLabel_en-US" xlink:label="lab_ecd_PnsnAdjsPrrSvcCstMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Pension Adjustments Prior Service Cost</link:label>
    <link:label id="lab_ecd_PnsnAdjsPrrSvcCstMember_label_en-US" xlink:label="lab_ecd_PnsnAdjsPrrSvcCstMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Pension Adjustments Prior Service Cost [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_PnsnAdjsPrrSvcCstMember" xlink:href="https://xbrl.sec.gov/ecd/2024/ecd-2024.xsd#ecd_PnsnAdjsPrrSvcCstMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_PnsnAdjsPrrSvcCstMember" xlink:to="lab_ecd_PnsnAdjsPrrSvcCstMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DefinedBenefitPlanFairValueOfPlanAssets_57acae15-46a9-4e3d-b1f1-f8d20bb4a5ee_periodStartLabel_en-US" xlink:label="lab_us-gaap_DefinedBenefitPlanFairValueOfPlanAssets" xlink:role="http://www.xbrl.org/2003/role/periodStartLabel" xlink:type="resource" xml:lang="en-US">Fair value of assets, beginning of period</link:label>
    <link:label id="lab_us-gaap_DefinedBenefitPlanFairValueOfPlanAssets_7e6313f9-dd49-43ab-9399-6bd7caad54d7_periodEndLabel_en-US" xlink:label="lab_us-gaap_DefinedBenefitPlanFairValueOfPlanAssets" xlink:role="http://www.xbrl.org/2003/role/periodEndLabel" xlink:type="resource" xml:lang="en-US">Fair value of assets, end of period</link:label>
    <link:label id="lab_us-gaap_DefinedBenefitPlanFairValueOfPlanAssets_3d820f51-565a-4eef-9c1a-1cc6c30d7e95_terseLabel_en-US" xlink:label="lab_us-gaap_DefinedBenefitPlanFairValueOfPlanAssets" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Defined Benefit Plan, Plan Assets, Amount</link:label>
    <link:label id="lab_us-gaap_DefinedBenefitPlanFairValueOfPlanAssets_label_en-US" xlink:label="lab_us-gaap_DefinedBenefitPlanFairValueOfPlanAssets" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Defined Benefit Plan, Plan Assets, Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DefinedBenefitPlanFairValueOfPlanAssets" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_DefinedBenefitPlanFairValueOfPlanAssets"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DefinedBenefitPlanFairValueOfPlanAssets" xlink:to="lab_us-gaap_DefinedBenefitPlanFairValueOfPlanAssets" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalAfterYearFive_d437d701-0782-4b3b-b1b4-a280d4f6abfb_terseLabel_en-US" xlink:label="lab_us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalAfterYearFive" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Long-Term Debt, Maturity, after Year Five</link:label>
    <link:label id="lab_us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalAfterYearFive_label_en-US" xlink:label="lab_us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalAfterYearFive" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Long-Term Debt, Maturity, after Year Five</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalAfterYearFive" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalAfterYearFive"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalAfterYearFive" xlink:to="lab_us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalAfterYearFive" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LiabilitiesOfDisposalGroupIncludingDiscontinuedOperationCurrent_2da5190c-46ca-4359-8c67-89991db575ec_terseLabel_en-US" xlink:label="lab_us-gaap_LiabilitiesOfDisposalGroupIncludingDiscontinuedOperationCurrent" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Current liabilities of discontinued operations</link:label>
    <link:label id="lab_us-gaap_LiabilitiesOfDisposalGroupIncludingDiscontinuedOperationCurrent_label_en-US" xlink:label="lab_us-gaap_LiabilitiesOfDisposalGroupIncludingDiscontinuedOperationCurrent" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Disposal Group, Including Discontinued Operation, Liabilities, Current</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LiabilitiesOfDisposalGroupIncludingDiscontinuedOperationCurrent" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_LiabilitiesOfDisposalGroupIncludingDiscontinuedOperationCurrent"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LiabilitiesOfDisposalGroupIncludingDiscontinuedOperationCurrent" xlink:to="lab_us-gaap_LiabilitiesOfDisposalGroupIncludingDiscontinuedOperationCurrent" xlink:type="arc" order="1"/>
    <link:label id="lab_codi_VendorMember_c5e9e961-ed54-4760-b102-80ac683baaa8_terseLabel_en-US" xlink:label="lab_codi_VendorMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Vendor</link:label>
    <link:label id="lab_codi_VendorMember_label_en-US" xlink:label="lab_codi_VendorMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Vendor [Member]</link:label>
    <link:label id="lab_codi_VendorMember_documentation_en-US" xlink:label="lab_codi_VendorMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Vendor [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_codi_VendorMember" xlink:href="codi-20241231.xsd#codi_VendorMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_codi_VendorMember" xlink:to="lab_codi_VendorMember" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_PnsnBnftsAdjFnTextBlock_terseLabel_en-US" xlink:label="lab_ecd_PnsnBnftsAdjFnTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Pension Benefits Adjustments, Footnote</link:label>
    <link:label id="lab_ecd_PnsnBnftsAdjFnTextBlock_label_en-US" xlink:label="lab_ecd_PnsnBnftsAdjFnTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Pension Benefits Adjustments, Footnote [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_PnsnBnftsAdjFnTextBlock" xlink:href="https://xbrl.sec.gov/ecd/2024/ecd-2024.xsd#ecd_PnsnBnftsAdjFnTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_PnsnBnftsAdjFnTextBlock" xlink:to="lab_ecd_PnsnBnftsAdjFnTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_TotalShareholderRtnVsPeerGroupTextBlock_terseLabel_en-US" xlink:label="lab_ecd_TotalShareholderRtnVsPeerGroupTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Total Shareholder Return Vs Peer Group</link:label>
    <link:label id="lab_ecd_TotalShareholderRtnVsPeerGroupTextBlock_label_en-US" xlink:label="lab_ecd_TotalShareholderRtnVsPeerGroupTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Total Shareholder Return Vs Peer Group [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_TotalShareholderRtnVsPeerGroupTextBlock" xlink:href="https://xbrl.sec.gov/ecd/2024/ecd-2024.xsd#ecd_TotalShareholderRtnVsPeerGroupTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_TotalShareholderRtnVsPeerGroupTextBlock" xlink:to="lab_ecd_TotalShareholderRtnVsPeerGroupTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_PaymentsForCommissions_f1c4aff7-a927-441b-a896-1fd7f7bd8d47_terseLabel_en-US" xlink:label="lab_us-gaap_PaymentsForCommissions" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Payments for Commissions</link:label>
    <link:label id="lab_us-gaap_PaymentsForCommissions_label_en-US" xlink:label="lab_us-gaap_PaymentsForCommissions" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Payments for Commissions</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PaymentsForCommissions" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_PaymentsForCommissions"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PaymentsForCommissions" xlink:to="lab_us-gaap_PaymentsForCommissions" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_DocumentAnnualReport_0cc24ce3-08f4-4437-b48a-313f09663864_terseLabel_en-US" xlink:label="lab_dei_DocumentAnnualReport" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Document Quarterly Report</link:label>
    <link:label id="lab_dei_DocumentAnnualReport_label_en-US" xlink:label="lab_dei_DocumentAnnualReport" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Document Annual Report</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_DocumentAnnualReport" xlink:href="https://xbrl.sec.gov/dei/2024/dei-2024.xsd#dei_DocumentAnnualReport"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_DocumentAnnualReport" xlink:to="lab_dei_DocumentAnnualReport" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FinanceLeaseLiabilityPaymentsDueYearThree_d06f3a52-0150-442e-8cc4-ce1f5aa59cfb_terseLabel_en-US" xlink:label="lab_us-gaap_FinanceLeaseLiabilityPaymentsDueYearThree" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Finance Lease, Liability, to be Paid, Year Three</link:label>
    <link:label id="lab_us-gaap_FinanceLeaseLiabilityPaymentsDueYearThree_label_en-US" xlink:label="lab_us-gaap_FinanceLeaseLiabilityPaymentsDueYearThree" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Finance Lease, Liability, to be Paid, Year Three</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FinanceLeaseLiabilityPaymentsDueYearThree" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_FinanceLeaseLiabilityPaymentsDueYearThree"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FinanceLeaseLiabilityPaymentsDueYearThree" xlink:to="lab_us-gaap_FinanceLeaseLiabilityPaymentsDueYearThree" xlink:type="arc" order="1"/>
    <link:label id="lab_codi_AccruedDistributionPreferredShareholders_3712d001-2644-479c-be54-489a6e8c538e_terseLabel_en-US" xlink:label="lab_codi_AccruedDistributionPreferredShareholders" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Dividends, Preferred Stock, Cash</link:label>
    <link:label id="lab_codi_AccruedDistributionPreferredShareholders_label_en-US" xlink:label="lab_codi_AccruedDistributionPreferredShareholders" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Accrued Distribution Preferred Shareholders</link:label>
    <link:label id="lab_codi_AccruedDistributionPreferredShareholders_documentation_en-US" xlink:label="lab_codi_AccruedDistributionPreferredShareholders" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Accrued Distribution Preferred Shareholders</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_codi_AccruedDistributionPreferredShareholders" xlink:href="codi-20241231.xsd#codi_AccruedDistributionPreferredShareholders"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_codi_AccruedDistributionPreferredShareholders" xlink:to="lab_codi_AccruedDistributionPreferredShareholders" xlink:type="arc" order="1"/>
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    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DiscontinuedOperationTaxExpenseBenefitFromProvisionForGainLossOnDisposal" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_DiscontinuedOperationTaxExpenseBenefitFromProvisionForGainLossOnDisposal"/>
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    <link:label id="lab_codi_StockholdersEquityTable_documentation_en-US" xlink:label="lab_codi_StockholdersEquityTable" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Stockholders Equity [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_codi_StockholdersEquityTable" xlink:href="codi-20241231.xsd#codi_StockholdersEquityTable"/>
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    <link:label id="lab_us-gaap_ParentMember_276814f6-0db5-4499-af42-8d73317e3e50_terseLabel_en-US" xlink:label="lab_us-gaap_ParentMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Stockholders' Equity Attributable to Holdings</link:label>
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    <link:label id="lab_us-gaap_ParentMember_label_en-US" xlink:label="lab_us-gaap_ParentMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Parent [Member]</link:label>
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    <link:label id="lab_us-gaap_AmortizationOfIntangibleAssets_label_en-US" xlink:label="lab_us-gaap_AmortizationOfIntangibleAssets" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Amortization of Intangible Assets</link:label>
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    <link:label id="lab_us-gaap_CommonStockNoParValue_692151fa-fa51-4b1a-9fd0-4db12aec09b6_terseLabel_en-US" xlink:label="lab_us-gaap_CommonStockNoParValue" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Trust shares, par value (in dollars per share)</link:label>
    <link:label id="lab_us-gaap_CommonStockNoParValue_label_en-US" xlink:label="lab_us-gaap_CommonStockNoParValue" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Common Stock, No Par Value</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CommonStockNoParValue" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_CommonStockNoParValue"/>
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    <link:label id="lab_us-gaap_MovementInValuationAllowancesAndReservesRollForward_77bf915c-595b-46d2-abc8-b18359072179_terseLabel_en-US" xlink:label="lab_us-gaap_MovementInValuationAllowancesAndReservesRollForward" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">SEC Schedule, 12-09, Movement in Valuation Allowances and Reserves [Roll Forward]</link:label>
    <link:label id="lab_us-gaap_MovementInValuationAllowancesAndReservesRollForward_label_en-US" xlink:label="lab_us-gaap_MovementInValuationAllowancesAndReservesRollForward" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">SEC Schedule, 12-09, Movement in Valuation Allowances and Reserves [Roll Forward]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_MovementInValuationAllowancesAndReservesRollForward" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_MovementInValuationAllowancesAndReservesRollForward"/>
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    <link:label id="lab_codi_AtTheMarketEquityOfferingPreferredMember_b1356ca4-2299-4ab5-898a-6d682564cb97_terseLabel_en-US" xlink:label="lab_codi_AtTheMarketEquityOfferingPreferredMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">At the market equity offering - preferred</link:label>
    <link:label id="lab_codi_AtTheMarketEquityOfferingPreferredMember_label_en-US" xlink:label="lab_codi_AtTheMarketEquityOfferingPreferredMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">At the market equity offering - preferred [Member]</link:label>
    <link:label id="lab_codi_AtTheMarketEquityOfferingPreferredMember_documentation_en-US" xlink:label="lab_codi_AtTheMarketEquityOfferingPreferredMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">At the market equity offering - preferred</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_codi_AtTheMarketEquityOfferingPreferredMember" xlink:href="codi-20241231.xsd#codi_AtTheMarketEquityOfferingPreferredMember"/>
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    <link:label id="lab_us-gaap_AccountingPoliciesAbstract_1b3e959e-6b9c-4c26-b569-4390789a38e8_terseLabel_en-US" xlink:label="lab_us-gaap_AccountingPoliciesAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Accounting Policies [Abstract]</link:label>
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    <link:label id="lab_us-gaap_DebtInstrumentUnamortizedDiscount_9b428fb6-a389-45c1-96a1-7b205474bff2_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_DebtInstrumentUnamortizedDiscount" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Unamortized premiums and debt issuance costs</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtInstrumentUnamortizedDiscount" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_DebtInstrumentUnamortizedDiscount"/>
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    <link:label id="lab_us-gaap_LeaseholdImprovementsMember_633f17f7-0b6b-47ad-87d3-3312871b613e_terseLabel_en-US" xlink:label="lab_us-gaap_LeaseholdImprovementsMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Leasehold improvements</link:label>
    <link:label id="lab_us-gaap_LeaseholdImprovementsMember_label_en-US" xlink:label="lab_us-gaap_LeaseholdImprovementsMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Leasehold Improvements [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LeaseholdImprovementsMember" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_LeaseholdImprovementsMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LeaseholdImprovementsMember" xlink:to="lab_us-gaap_LeaseholdImprovementsMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_BusinessCombinationDisclosureTextBlock_8246f07b-fd37-4ee4-b1ca-97a44ec0d211_terseLabel_en-US" xlink:label="lab_us-gaap_BusinessCombinationDisclosureTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Acquisition of Businesses</link:label>
    <link:label id="lab_us-gaap_BusinessCombinationDisclosureTextBlock_label_en-US" xlink:label="lab_us-gaap_BusinessCombinationDisclosureTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Business Combination Disclosure [Text Block]</link:label>
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    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_BusinessCombinationDisclosureTextBlock" xlink:to="lab_us-gaap_BusinessCombinationDisclosureTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_CurrentFiscalYearEndDate_0ad8f3df-e860-482f-ae7f-0d6f484a9ccd_terseLabel_en-US" xlink:label="lab_dei_CurrentFiscalYearEndDate" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Current Fiscal Year End Date</link:label>
    <link:label id="lab_dei_CurrentFiscalYearEndDate_label_en-US" xlink:label="lab_dei_CurrentFiscalYearEndDate" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Current Fiscal Year End Date</link:label>
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    <link:label id="lab_us-gaap_ValuationAllowancesAndReservesBalance_1928022f-c6f6-4bce-a27e-8e6ff705ea87_periodStartLabel_en-US" xlink:label="lab_us-gaap_ValuationAllowancesAndReservesBalance" xlink:role="http://www.xbrl.org/2003/role/periodStartLabel" xlink:type="resource" xml:lang="en-US">Balance at beginning of year</link:label>
    <link:label id="lab_us-gaap_ValuationAllowancesAndReservesBalance_88db8368-1f5e-499f-be43-7f61e1c0c159_periodEndLabel_en-US" xlink:label="lab_us-gaap_ValuationAllowancesAndReservesBalance" xlink:role="http://www.xbrl.org/2003/role/periodEndLabel" xlink:type="resource" xml:lang="en-US">Balance at end of Year</link:label>
    <link:label id="lab_us-gaap_ValuationAllowancesAndReservesBalance_label_en-US" xlink:label="lab_us-gaap_ValuationAllowancesAndReservesBalance" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">SEC Schedule, 12-09, Valuation Allowances and Reserves, Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ValuationAllowancesAndReservesBalance" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_ValuationAllowancesAndReservesBalance"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ValuationAllowancesAndReservesBalance" xlink:to="lab_us-gaap_ValuationAllowancesAndReservesBalance" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LesseeOperatingLeaseLiabilityUndiscountedExcessAmount_09408a9b-ba34-4f89-919d-b47809cd4185_terseLabel_en-US" xlink:label="lab_us-gaap_LesseeOperatingLeaseLiabilityUndiscountedExcessAmount" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Less: Interest</link:label>
    <link:label id="lab_us-gaap_LesseeOperatingLeaseLiabilityUndiscountedExcessAmount_label_en-US" xlink:label="lab_us-gaap_LesseeOperatingLeaseLiabilityUndiscountedExcessAmount" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Lessee, Operating Lease, Liability, Undiscounted Excess Amount</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_ecd_PeoName" xlink:href="https://xbrl.sec.gov/ecd/2024/ecd-2024.xsd#ecd_PeoName"/>
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    <link:label id="lab_us-gaap_ShareBasedCompensationArrangementsByShareBasedPaymentAwardAwardTypeAndPlanNameDomain_label_en-US" xlink:label="lab_us-gaap_ShareBasedCompensationArrangementsByShareBasedPaymentAwardAwardTypeAndPlanNameDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Award Type [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ShareBasedCompensationArrangementsByShareBasedPaymentAwardAwardTypeAndPlanNameDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_ShareBasedCompensationArrangementsByShareBasedPaymentAwardAwardTypeAndPlanNameDomain"/>
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    <link:label id="lab_us-gaap_DisposalGroupIncludingDiscontinuedOperationAccountsNotesAndLoansReceivableNet_f75af6f8-47a0-46f7-8f58-2d53007c95a9_terseLabel_en-US" xlink:label="lab_us-gaap_DisposalGroupIncludingDiscontinuedOperationAccountsNotesAndLoansReceivableNet" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Accounts receivable, net</link:label>
    <link:label id="lab_us-gaap_DisposalGroupIncludingDiscontinuedOperationAccountsNotesAndLoansReceivableNet_label_en-US" xlink:label="lab_us-gaap_DisposalGroupIncludingDiscontinuedOperationAccountsNotesAndLoansReceivableNet" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Disposal Group, Including Discontinued Operation, Accounts, Notes and Loans Receivable, Net</link:label>
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    <link:label id="lab_us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedCashAndEquivalents_a5f5a1d7-adc2-41cf-9852-619de97dd876_terseLabel_en-US" xlink:label="lab_us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedCashAndEquivalents" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Cash</link:label>
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    <link:label id="lab_us-gaap_IncomeLossFromDiscontinuedOperationsNetOfTaxAttributableToReportingEntity_dc8824b6-e4f0-464e-89eb-7528af3aeb54_terseLabel_en-US" xlink:label="lab_us-gaap_IncomeLossFromDiscontinuedOperationsNetOfTaxAttributableToReportingEntity" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Income (loss) from discontinued operations, net of income tax</link:label>
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    <link:label id="lab_codi_DistributionsForContributionBasedProfitAllocationPayments_7793f8c1-b6b0-454d-8a2a-0e6ddbdc4b24_terseLabel_en-US" xlink:label="lab_codi_DistributionsForContributionBasedProfitAllocationPayments" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Distributions For Contribution Based Profit Allocation Payments</link:label>
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    <link:label id="lab_us-gaap_IncomeTaxesPaid_f226d578-c356-4e7d-9c14-696f1acdd14c_terseLabel_en-US" xlink:label="lab_us-gaap_IncomeTaxesPaid" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Taxes paid</link:label>
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    <link:label id="lab_codi_TermLoanFacilityMember_770ca17e-9632-4bd7-9ea3-6d640f7618a5_terseLabel_en-US" xlink:label="lab_codi_TermLoanFacilityMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Term Loan Facility</link:label>
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    <link:label id="lab_codi_TermLoanFacilityMember_documentation_en-US" xlink:label="lab_codi_TermLoanFacilityMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Term loan facility.</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DisaggregationOfRevenueTable" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_DisaggregationOfRevenueTable"/>
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    <link:label id="lab_us-gaap_ExtinguishmentOfDebtAxis_073b85d7-1c97-4b22-a6ce-747d47b83b1a_terseLabel_en-US" xlink:label="lab_us-gaap_ExtinguishmentOfDebtAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Extinguishment of Debt [Axis]</link:label>
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    <link:label id="lab_us-gaap_DisposalGroupIncludingDiscontinuedOperationOtherNoncurrentLiabilities_93507032-3a68-4668-9cf1-9bb66cf1575c_terseLabel_en-US" xlink:label="lab_us-gaap_DisposalGroupIncludingDiscontinuedOperationOtherNoncurrentLiabilities" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Disposal Group, Including Discontinued Operation, Other Liabilities, Noncurrent</link:label>
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    <link:label id="lab_codi_VelocityOutdoorMember_c2f4833f-c8ef-42e3-8d1e-852e646b1388_terseLabel_en-US" xlink:label="lab_codi_VelocityOutdoorMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Velocity Outdoor [Member]</link:label>
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    <link:label id="lab_codi_VelocityOutdoorMember_label_en-US" xlink:label="lab_codi_VelocityOutdoorMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Velocity Outdoor [Member]</link:label>
    <link:label id="lab_codi_VelocityOutdoorMember_documentation_en-US" xlink:label="lab_codi_VelocityOutdoorMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Velocity Outdoor [Member]</link:label>
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    <link:label id="lab_codi_DeferredTaxLiabilitiesPrepaidAndOtherExpenses_documentation_en-US" xlink:label="lab_codi_DeferredTaxLiabilitiesPrepaidAndOtherExpenses" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Deferred tax liabilities prepaid and other expenses.</link:label>
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    <link:label id="lab_us-gaap_BusinessCombinationProvisionalInformationInitialAccountingIncompleteAdjustmentFinancialLiabilities_12207502-f28c-4e36-92ba-06d7712bd2fc_terseLabel_en-US" xlink:label="lab_us-gaap_BusinessCombinationProvisionalInformationInitialAccountingIncompleteAdjustmentFinancialLiabilities" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Business Combination, Provisional Information, Initial Accounting Incomplete, Adjustment, Financial Liabilities</link:label>
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    <link:label id="lab_us-gaap_SeriesCPreferredStockMember_348a4002-e945-4479-8193-8dbad0726a44_terseLabel_en-US" xlink:label="lab_us-gaap_SeriesCPreferredStockMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Series C Preferred Stock [Member]</link:label>
    <link:label id="lab_us-gaap_SeriesCPreferredStockMember_label_en-US" xlink:label="lab_us-gaap_SeriesCPreferredStockMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Series C Preferred Stock [Member]</link:label>
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    <link:label id="lab_codi_DefinedContributionPlanEmployerContributionAmount_536991c0-c713-4c20-934e-e7b8d71dc4eb_terseLabel_en-US" xlink:label="lab_codi_DefinedContributionPlanEmployerContributionAmount" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Total employer contributions to plans</link:label>
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    <link:label id="lab_codi_DefinedContributionPlanEmployerContributionAmount_documentation_en-US" xlink:label="lab_codi_DefinedContributionPlanEmployerContributionAmount" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Defined contribution plan employer contribution amount.</link:label>
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    <link:label id="lab_us-gaap_DeferredTaxAssetsInProcessResearchAndDevelopment_dd9200fe-aad5-4045-8c10-95e797de0f97_terseLabel_en-US" xlink:label="lab_us-gaap_DeferredTaxAssetsInProcessResearchAndDevelopment" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Deferred Tax Asset, In-Process Research and Development</link:label>
    <link:label id="lab_us-gaap_DeferredTaxAssetsInProcessResearchAndDevelopment_label_en-US" xlink:label="lab_us-gaap_DeferredTaxAssetsInProcessResearchAndDevelopment" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Deferred Tax Asset, In-Process Research and Development</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DeferredTaxAssetsInProcessResearchAndDevelopment" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_DeferredTaxAssetsInProcessResearchAndDevelopment"/>
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    <link:label id="lab_us-gaap_PreferredStockDividendRatePercentage_965ffad6-d607-4351-af43-7ee1d4457eb2_terseLabel_en-US" xlink:label="lab_us-gaap_PreferredStockDividendRatePercentage" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Preferred Stock, Dividend Rate, Percentage</link:label>
    <link:label id="lab_us-gaap_PreferredStockDividendRatePercentage_label_en-US" xlink:label="lab_us-gaap_PreferredStockDividendRatePercentage" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Preferred Stock, Dividend Rate, Percentage</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PreferredStockDividendRatePercentage" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_PreferredStockDividendRatePercentage"/>
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    <link:label id="lab_srt_ScheduleOfValuationAndQualifyingAccountsDisclosureTextBlock_1cd8c013-a1af-4b0f-a089-05e472da4963_terseLabel_en-US" xlink:label="lab_srt_ScheduleOfValuationAndQualifyingAccountsDisclosureTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Valuation and Qualifying Accounts</link:label>
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    <link:label id="lab_us-gaap_ProceedsFromDivestitureOfBusinessesAndInterestsInAffiliates_19404b95-bba1-4d70-b479-15daad6a194b_verboseLabel_en-US" xlink:label="lab_us-gaap_ProceedsFromDivestitureOfBusinessesAndInterestsInAffiliates" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Proceeds from sale of businesses</link:label>
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    <link:label id="lab_dei_AuditorFirmId_5c66795d-4486-4fe0-9995-d0af628ce5ae_terseLabel_en-US" xlink:label="lab_dei_AuditorFirmId" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Auditor Firm ID</link:label>
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    <link:label id="lab_us-gaap_OperatingIncomeLoss_label_en-US" xlink:label="lab_us-gaap_OperatingIncomeLoss" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Operating Income (Loss)</link:label>
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    <link:label id="lab_us-gaap_FairValueByFairValueHierarchyLevelAxis_38ae5dfc-07f8-41e7-a954-4a5f1a6637d7_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueByFairValueHierarchyLevelAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Fair Value Hierarchy and NAV [Axis]</link:label>
    <link:label id="lab_us-gaap_FairValueByFairValueHierarchyLevelAxis_label_en-US" xlink:label="lab_us-gaap_FairValueByFairValueHierarchyLevelAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fair Value Hierarchy and NAV [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueByFairValueHierarchyLevelAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_FairValueByFairValueHierarchyLevelAxis"/>
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    <link:label id="lab_us-gaap_CommissionsPayableToBrokerDealersAndClearingOrganizations_8bc117ee-1656-4f2b-917a-0db7b1e215de_terseLabel_en-US" xlink:label="lab_us-gaap_CommissionsPayableToBrokerDealersAndClearingOrganizations" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Commissions Payable to Broker-Dealers and Clearing Organizations</link:label>
    <link:label id="lab_us-gaap_CommissionsPayableToBrokerDealersAndClearingOrganizations_label_en-US" xlink:label="lab_us-gaap_CommissionsPayableToBrokerDealersAndClearingOrganizations" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Commission Payable to Broker-Dealer and Clearing Organization</link:label>
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    <link:label id="lab_codi_DisposalGroupTotalenterprisevalue_003850d5-a1ed-45b5-8518-0ed0bdff0d56_terseLabel_en-US" xlink:label="lab_codi_DisposalGroupTotalenterprisevalue" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Disposal Group, Total enterprise value</link:label>
    <link:label id="lab_codi_DisposalGroupTotalenterprisevalue_label_en-US" xlink:label="lab_codi_DisposalGroupTotalenterprisevalue" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Disposal Group, Total enterprise value</link:label>
    <link:label id="lab_codi_DisposalGroupTotalenterprisevalue_documentation_en-US" xlink:label="lab_codi_DisposalGroupTotalenterprisevalue" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Disposal Group, Total enterprise value</link:label>
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    <link:label id="lab_us-gaap_FinanceLeaseLiabilityPaymentsDueYearTwo_1dab46fb-8784-421f-9b69-2b3b7fc18625_terseLabel_en-US" xlink:label="lab_us-gaap_FinanceLeaseLiabilityPaymentsDueYearTwo" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Finance Lease, Liability, to be Paid, Year Two</link:label>
    <link:label id="lab_us-gaap_FinanceLeaseLiabilityPaymentsDueYearTwo_label_en-US" xlink:label="lab_us-gaap_FinanceLeaseLiabilityPaymentsDueYearTwo" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Finance Lease, Liability, to be Paid, Year Two</link:label>
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    <link:label id="lab_us-gaap_IncomeLossFromDiscontinuedOperationsNetOfTax_2d27e9aa-5a8d-4de1-b42e-1e2dd0e726bb_terseLabel_en-US" xlink:label="lab_us-gaap_IncomeLossFromDiscontinuedOperationsNetOfTax" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Income (loss) from discontinued operations, net of income tax</link:label>
    <link:label id="lab_us-gaap_IncomeLossFromDiscontinuedOperationsNetOfTax_label_en-US" xlink:label="lab_us-gaap_IncomeLossFromDiscontinuedOperationsNetOfTax" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Income (Loss) from Discontinued Operations, Net of Tax, Including Portion Attributable to Noncontrolling Interest</link:label>
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    <link:label id="lab_us-gaap_FiniteLivedIntangibleAssetsMajorClassNameDomain_ac71c127-fb80-4821-aecc-67c5c01548c0_terseLabel_en-US" xlink:label="lab_us-gaap_FiniteLivedIntangibleAssetsMajorClassNameDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Finite-Lived Intangible Assets, Major Class Name [Domain]</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_EffectiveIncomeTaxRateReconciliationRepatriationOfForeignEarnings" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_EffectiveIncomeTaxRateReconciliationRepatriationOfForeignEarnings"/>
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    <link:label id="lab_us-gaap_RightOfUseAssetObtainedInExchangeForOperatingLeaseLiability_2df03ebe-8465-4958-9b2a-c0589a3c208c_terseLabel_en-US" xlink:label="lab_us-gaap_RightOfUseAssetObtainedInExchangeForOperatingLeaseLiability" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Right-of-Use Asset Obtained in Exchange for Operating Lease Liability</link:label>
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    <link:label id="lab_us-gaap_EquitySecuritiesByIndustryAxis_97668889-8b5b-4ebf-bdd4-5ac470b1e160_terseLabel_en-US" xlink:label="lab_us-gaap_EquitySecuritiesByIndustryAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Industry Sector [Axis]</link:label>
    <link:label id="lab_us-gaap_EquitySecuritiesByIndustryAxis_label_en-US" xlink:label="lab_us-gaap_EquitySecuritiesByIndustryAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Industry Sector [Axis]</link:label>
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    <link:label id="lab_us-gaap_DefinedBenefitPlanExpectedReturnOnPlanAssets_29a95394-2eaf-493c-9cc2-505c89f63c81_negatedLabel_en-US" xlink:label="lab_us-gaap_DefinedBenefitPlanExpectedReturnOnPlanAssets" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:type="resource" xml:lang="en-US">Expected return on plan assets</link:label>
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    <link:label id="lab_us-gaap_PropertyPlantAndEquipmentLineItems_6036c70b-948d-4e2a-96d7-2e80df0eeaa2_terseLabel_en-US" xlink:label="lab_us-gaap_PropertyPlantAndEquipmentLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Property, Plant and Equipment [Line Items]</link:label>
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    <link:label id="lab_codi_DistributionToShareholders_documentation_en-US" xlink:label="lab_codi_DistributionToShareholders" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Distribution to shareholders.</link:label>
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    <link:label id="lab_us-gaap_GoodwillMember_label_en-US" xlink:label="lab_us-gaap_GoodwillMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Goodwill [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_GoodwillMember" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_GoodwillMember"/>
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    <link:label id="lab_us-gaap_FinanceLeaseLiability_4dd3e0fa-4c8a-4da3-90f8-f08d5d2739c8_terseLabel_en-US" xlink:label="lab_us-gaap_FinanceLeaseLiability" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Finance Lease, Liability</link:label>
    <link:label id="lab_us-gaap_FinanceLeaseLiability_label_en-US" xlink:label="lab_us-gaap_FinanceLeaseLiability" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Finance Lease, Liability</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FinanceLeaseLiability" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_FinanceLeaseLiability"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FinanceLeaseLiability" xlink:to="lab_us-gaap_FinanceLeaseLiability" xlink:type="arc" order="1"/>
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    <link:label id="lab_us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseYearFour_label_en-US" xlink:label="lab_us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseYearFour" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Finite-Lived Intangible Asset, Expected Amortization, Year Four</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseYearFour" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseYearFour"/>
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    <link:label id="lab_ecd_AllIndividualsMember_label_en-US" xlink:label="lab_ecd_AllIndividualsMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">All Individuals [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_AllIndividualsMember" xlink:href="https://xbrl.sec.gov/ecd/2024/ecd-2024.xsd#ecd_AllIndividualsMember"/>
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    <link:label id="lab_us-gaap_StandardProductWarrantyAccrualPreexistingIncreaseDecrease_cb84cbe4-4e87-41f2-b128-dbd119d4d234_terseLabel_en-US" xlink:label="lab_us-gaap_StandardProductWarrantyAccrualPreexistingIncreaseDecrease" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Accrual</link:label>
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    <link:label id="lab_us-gaap_ReportingUnitAxis_f7665919-ca34-41a4-a513-3441efe84de2_terseLabel_en-US" xlink:label="lab_us-gaap_ReportingUnitAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Reporting Unit [Axis]</link:label>
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    <link:label id="lab_us-gaap_EffectiveIncomeTaxRateReconciliationDispositionOfBusiness_ca019e08-1574-4369-be61-0e19cefcaa43_terseLabel_en-US" xlink:label="lab_us-gaap_EffectiveIncomeTaxRateReconciliationDispositionOfBusiness" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Effective Income Tax Rate Reconciliation, Disposition of Business, Percent</link:label>
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    <link:label id="lab_us-gaap_AccountsReceivableGross_0df9b022-c7c1-40af-a8ac-5b994455c1c7_terseLabel_en-US" xlink:label="lab_us-gaap_AccountsReceivableGross" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Accounts Receivable, before Allowance for Credit Loss</link:label>
    <link:label id="lab_us-gaap_AccountsReceivableGross_label_en-US" xlink:label="lab_us-gaap_AccountsReceivableGross" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Accounts Receivable, before Allowance for Credit Loss</link:label>
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    <link:label id="lab_us-gaap_DebtInstrumentTable_a2bb7917-8ed4-4ac6-b443-cd6276e9f67b_terseLabel_en-US" xlink:label="lab_us-gaap_DebtInstrumentTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Long-term Debt Instruments [Table]</link:label>
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    <link:label id="lab_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearFour_471f553c-f30a-4681-aca6-97e2a8f03f73_terseLabel_en-US" xlink:label="lab_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearFour" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">2023</link:label>
    <link:label id="lab_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearFour_label_en-US" xlink:label="lab_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearFour" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Lessee, Operating Lease, Liability, to be Paid, Year Four</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearFour" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearFour"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearFour" xlink:to="lab_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearFour" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AccrualForTaxesOtherThanIncomeTaxesCurrent_41a11a76-ffab-4fed-b4a5-c353d022eb96_terseLabel_en-US" xlink:label="lab_us-gaap_AccrualForTaxesOtherThanIncomeTaxesCurrent" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Accrued taxes</link:label>
    <link:label id="lab_us-gaap_AccrualForTaxesOtherThanIncomeTaxesCurrent_label_en-US" xlink:label="lab_us-gaap_AccrualForTaxesOtherThanIncomeTaxesCurrent" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Accrual for Taxes Other than Income Taxes, Current</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AccrualForTaxesOtherThanIncomeTaxesCurrent" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_AccrualForTaxesOtherThanIncomeTaxesCurrent"/>
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    <link:label id="lab_us-gaap_RepaymentsOfLongTermLinesOfCredit_e684e273-9dad-45b6-8734-b1f5742a2998_negatedLabel_en-US" xlink:label="lab_us-gaap_RepaymentsOfLongTermLinesOfCredit" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:type="resource" xml:lang="en-US">Repayments under credit facility</link:label>
    <link:label id="lab_us-gaap_RepaymentsOfLongTermLinesOfCredit_label_en-US" xlink:label="lab_us-gaap_RepaymentsOfLongTermLinesOfCredit" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Repayments of Long-Term Lines of Credit</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_RepaymentsOfLongTermLinesOfCredit" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_RepaymentsOfLongTermLinesOfCredit"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_RepaymentsOfLongTermLinesOfCredit" xlink:to="lab_us-gaap_RepaymentsOfLongTermLinesOfCredit" xlink:type="arc" order="1"/>
    <link:label id="lab_codi_AtTheMarketOfferingCosts_2995d760-224f-41aa-90f1-bb0415c5f0b9_terseLabel_en-US" xlink:label="lab_codi_AtTheMarketOfferingCosts" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">At the market offering costs</link:label>
    <link:label id="lab_codi_AtTheMarketOfferingCosts_label_en-US" xlink:label="lab_codi_AtTheMarketOfferingCosts" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">At the market offering costs</link:label>
    <link:label id="lab_codi_AtTheMarketOfferingCosts_documentation_en-US" xlink:label="lab_codi_AtTheMarketOfferingCosts" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">At the market offering costs</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_codi_AtTheMarketOfferingCosts" xlink:href="codi-20241231.xsd#codi_AtTheMarketOfferingCosts"/>
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    <link:label id="lab_us-gaap_OtherNoncurrentLiabilitiesMember_d8c98551-acd6-4b39-8a4f-2ef87d95e961_terseLabel_en-US" xlink:label="lab_us-gaap_OtherNoncurrentLiabilitiesMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Long-term debt</link:label>
    <link:label id="lab_us-gaap_OtherNoncurrentLiabilitiesMember_label_en-US" xlink:label="lab_us-gaap_OtherNoncurrentLiabilitiesMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Other Noncurrent Liabilities [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OtherNoncurrentLiabilitiesMember" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_OtherNoncurrentLiabilitiesMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OtherNoncurrentLiabilitiesMember" xlink:to="lab_us-gaap_OtherNoncurrentLiabilitiesMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OrganizationConsolidationAndPresentationOfFinancialStatementsAbstract_22dfe844-e11e-4d1b-9e52-28bb7775bb1c_terseLabel_en-US" xlink:label="lab_us-gaap_OrganizationConsolidationAndPresentationOfFinancialStatementsAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Organization, Consolidation and Presentation of Financial Statements [Abstract]</link:label>
    <link:label id="lab_us-gaap_OrganizationConsolidationAndPresentationOfFinancialStatementsAbstract_label_en-US" xlink:label="lab_us-gaap_OrganizationConsolidationAndPresentationOfFinancialStatementsAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Organization, Consolidation and Presentation of Financial Statements [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OrganizationConsolidationAndPresentationOfFinancialStatementsAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_OrganizationConsolidationAndPresentationOfFinancialStatementsAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OrganizationConsolidationAndPresentationOfFinancialStatementsAbstract" xlink:to="lab_us-gaap_OrganizationConsolidationAndPresentationOfFinancialStatementsAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OperatingLeaseWeightedAverageDiscountRatePercent_4147ecdf-f024-4d2a-830e-954c612e97e5_terseLabel_en-US" xlink:label="lab_us-gaap_OperatingLeaseWeightedAverageDiscountRatePercent" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Operating Lease, Weighted Average Discount Rate, Percent</link:label>
    <link:label id="lab_us-gaap_OperatingLeaseWeightedAverageDiscountRatePercent_label_en-US" xlink:label="lab_us-gaap_OperatingLeaseWeightedAverageDiscountRatePercent" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Operating Lease, Weighted Average Discount Rate, Percent</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OperatingLeaseWeightedAverageDiscountRatePercent" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_OperatingLeaseWeightedAverageDiscountRatePercent"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OperatingLeaseWeightedAverageDiscountRatePercent" xlink:to="lab_us-gaap_OperatingLeaseWeightedAverageDiscountRatePercent" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_NetCashProvidedByUsedInFinancingActivities_f9bb162b-0895-4320-8889-48c0771493b8_totalLabel_en-US" xlink:label="lab_us-gaap_NetCashProvidedByUsedInFinancingActivities" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Net cash provided by (used in) financing activities</link:label>
    <link:label id="lab_us-gaap_NetCashProvidedByUsedInFinancingActivities_label_en-US" xlink:label="lab_us-gaap_NetCashProvidedByUsedInFinancingActivities" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Net Cash Provided by (Used in) Financing Activities</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_NetCashProvidedByUsedInFinancingActivities" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_NetCashProvidedByUsedInFinancingActivities"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_NetCashProvidedByUsedInFinancingActivities" xlink:to="lab_us-gaap_NetCashProvidedByUsedInFinancingActivities" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CreditFacilityAxis_70dbe777-c143-4797-8179-14392035e416_terseLabel_en-US" xlink:label="lab_us-gaap_CreditFacilityAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Credit Facility [Axis]</link:label>
    <link:label id="lab_us-gaap_CreditFacilityAxis_label_en-US" xlink:label="lab_us-gaap_CreditFacilityAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Credit Facility [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CreditFacilityAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_CreditFacilityAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CreditFacilityAxis" xlink:to="lab_us-gaap_CreditFacilityAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LongTermDebtFairValue_8f7d893c-a2d7-4317-96ae-76f54750d358_terseLabel_en-US" xlink:label="lab_us-gaap_LongTermDebtFairValue" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Long-term Debt, Fair Value</link:label>
    <link:label id="lab_us-gaap_LongTermDebtFairValue_label_en-US" xlink:label="lab_us-gaap_LongTermDebtFairValue" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Long-Term Debt, Fair Value</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LongTermDebtFairValue" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_LongTermDebtFairValue"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LongTermDebtFairValue" xlink:to="lab_us-gaap_LongTermDebtFairValue" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_EntityRegistrantName_cd0cee23-06d3-49ec-bdb9-f0984c4ae6e2_terseLabel_en-US" xlink:label="lab_dei_EntityRegistrantName" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Entity Registrant Name</link:label>
    <link:label id="lab_dei_EntityRegistrantName_label_en-US" xlink:label="lab_dei_EntityRegistrantName" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Entity Registrant Name</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityRegistrantName" xlink:href="https://xbrl.sec.gov/dei/2024/dei-2024.xsd#dei_EntityRegistrantName"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_EntityRegistrantName" xlink:to="lab_dei_EntityRegistrantName" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_AdjToNonPeoNeoCompFnTextBlock_terseLabel_en-US" xlink:label="lab_ecd_AdjToNonPeoNeoCompFnTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Adjustment to Non-PEO NEO Compensation Footnote</link:label>
    <link:label id="lab_ecd_AdjToNonPeoNeoCompFnTextBlock_label_en-US" xlink:label="lab_ecd_AdjToNonPeoNeoCompFnTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Adjustment to Non-PEO NEO Compensation Footnote [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_AdjToNonPeoNeoCompFnTextBlock" xlink:href="https://xbrl.sec.gov/ecd/2024/ecd-2024.xsd#ecd_AdjToNonPeoNeoCompFnTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_AdjToNonPeoNeoCompFnTextBlock" xlink:to="lab_ecd_AdjToNonPeoNeoCompFnTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DepreciationDepletionAndAmortization_91182620-96ec-44fd-9b49-3ca2809de998_terseLabel_en-US" xlink:label="lab_us-gaap_DepreciationDepletionAndAmortization" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Depreciation, Depletion and Amortization</link:label>
    <link:label id="lab_us-gaap_DepreciationDepletionAndAmortization_77d1cff5-f015-4e70-ad7c-aad8b91d3aa2_verboseLabel_en-US" xlink:label="lab_us-gaap_DepreciationDepletionAndAmortization" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Accumulated Depreciation, Depletion and Amortization, Period Increase (Decrease)</link:label>
    <link:label id="lab_us-gaap_DepreciationDepletionAndAmortization_label_en-US" xlink:label="lab_us-gaap_DepreciationDepletionAndAmortization" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Depreciation, Depletion and Amortization</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DepreciationDepletionAndAmortization" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_DepreciationDepletionAndAmortization"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DepreciationDepletionAndAmortization" xlink:to="lab_us-gaap_DepreciationDepletionAndAmortization" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_GrossProfit_31987ce8-6445-4097-abd6-aa348d9efcd0_totalLabel_en-US" xlink:label="lab_us-gaap_GrossProfit" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Gross profit</link:label>
    <link:label id="lab_us-gaap_GrossProfit_dead14ba-48f0-4a6e-92c7-835bac65a6d4_terseLabel_en-US" xlink:label="lab_us-gaap_GrossProfit" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Gross profit</link:label>
    <link:label id="lab_us-gaap_GrossProfit_label_en-US" xlink:label="lab_us-gaap_GrossProfit" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Gross Profit</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_GrossProfit" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_GrossProfit"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_GrossProfit" xlink:to="lab_us-gaap_GrossProfit" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DeferredStateAndLocalIncomeTaxExpenseBenefit_17efdecc-3dbd-42da-a6c2-6d5c65cb58a8_terseLabel_en-US" xlink:label="lab_us-gaap_DeferredStateAndLocalIncomeTaxExpenseBenefit" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">State</link:label>
    <link:label id="lab_us-gaap_DeferredStateAndLocalIncomeTaxExpenseBenefit_label_en-US" xlink:label="lab_us-gaap_DeferredStateAndLocalIncomeTaxExpenseBenefit" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Deferred State and Local Income Tax Expense (Benefit)</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DeferredStateAndLocalIncomeTaxExpenseBenefit" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_DeferredStateAndLocalIncomeTaxExpenseBenefit"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DeferredStateAndLocalIncomeTaxExpenseBenefit" xlink:to="lab_us-gaap_DeferredStateAndLocalIncomeTaxExpenseBenefit" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_AwardGrantDateFairValue_terseLabel_en-US" xlink:label="lab_ecd_AwardGrantDateFairValue" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Fair Value as of Grant Date</link:label>
    <link:label id="lab_ecd_AwardGrantDateFairValue_label_en-US" xlink:label="lab_ecd_AwardGrantDateFairValue" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Award Grant Date Fair Value</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_AwardGrantDateFairValue" xlink:href="https://xbrl.sec.gov/ecd/2024/ecd-2024.xsd#ecd_AwardGrantDateFairValue"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_AwardGrantDateFairValue" xlink:to="lab_ecd_AwardGrantDateFairValue" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_StockholdersEquityIncludingPortionAttributableToNoncontrollingInterestAbstract_9e203a19-411d-421d-86e2-b247061e4ae1_terseLabel_en-US" xlink:label="lab_us-gaap_StockholdersEquityIncludingPortionAttributableToNoncontrollingInterestAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Stockholders&#8217; equity</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_StockholdersEquityIncludingPortionAttributableToNoncontrollingInterestAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_StockholdersEquityIncludingPortionAttributableToNoncontrollingInterestAbstract"/>
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    <link:label id="lab_srt_SegmentGeographicalDomain_e72a1ebd-d78a-4af9-b1de-23831994c156_terseLabel_en-US" xlink:label="lab_srt_SegmentGeographicalDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Geographical [Domain]</link:label>
    <link:label id="lab_srt_SegmentGeographicalDomain_label_en-US" xlink:label="lab_srt_SegmentGeographicalDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Geographical [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_srt_SegmentGeographicalDomain" xlink:href="https://xbrl.fasb.org/srt/2024/elts/srt-2024.xsd#srt_SegmentGeographicalDomain"/>
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    <link:label id="lab_us-gaap_DisaggregationOfRevenueTableTextBlock_label_en-US" xlink:label="lab_us-gaap_DisaggregationOfRevenueTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Disaggregation of Revenue [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DisaggregationOfRevenueTableTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_DisaggregationOfRevenueTableTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DisaggregationOfRevenueTableTextBlock" xlink:to="lab_us-gaap_DisaggregationOfRevenueTableTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DisposalGroupIncludingDiscontinuedOperationIntangibleAssets_c643657c-8216-4250-9b1b-4a4de53482fd_terseLabel_en-US" xlink:label="lab_us-gaap_DisposalGroupIncludingDiscontinuedOperationIntangibleAssets" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Disposal Group, Including Discontinued Operation, Intangible Assets</link:label>
    <link:label id="lab_us-gaap_DisposalGroupIncludingDiscontinuedOperationIntangibleAssets_label_en-US" xlink:label="lab_us-gaap_DisposalGroupIncludingDiscontinuedOperationIntangibleAssets" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Disposal Group, Including Discontinued Operation, Intangible Assets</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DisposalGroupIncludingDiscontinuedOperationIntangibleAssets" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_DisposalGroupIncludingDiscontinuedOperationIntangibleAssets"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DisposalGroupIncludingDiscontinuedOperationIntangibleAssets" xlink:to="lab_us-gaap_DisposalGroupIncludingDiscontinuedOperationIntangibleAssets" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_StockIssuedDuringPeriodValueNewIssues_5acd12dc-04da-4df7-bfd9-6bfac88730a6_terseLabel_en-US" xlink:label="lab_us-gaap_StockIssuedDuringPeriodValueNewIssues" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Issuance of Trust common shares, net of offering costs</link:label>
    <link:label id="lab_us-gaap_StockIssuedDuringPeriodValueNewIssues_label_en-US" xlink:label="lab_us-gaap_StockIssuedDuringPeriodValueNewIssues" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Stock Issued During Period, Value, New Issues</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_StockIssuedDuringPeriodValueNewIssues" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_StockIssuedDuringPeriodValueNewIssues"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_StockIssuedDuringPeriodValueNewIssues" xlink:to="lab_us-gaap_StockIssuedDuringPeriodValueNewIssues" xlink:type="arc" order="1"/>
    <link:label id="lab_codi_KingsCamoMember_6fcb5ef4-fb6d-4007-85a8-01202d30abd9_terseLabel_en-US" xlink:label="lab_codi_KingsCamoMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">King's Camo</link:label>
    <link:label id="lab_codi_KingsCamoMember_label_en-US" xlink:label="lab_codi_KingsCamoMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">King's Camo [Member]</link:label>
    <link:label id="lab_codi_KingsCamoMember_documentation_en-US" xlink:label="lab_codi_KingsCamoMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">King's Camo</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_codi_KingsCamoMember" xlink:href="codi-20241231.xsd#codi_KingsCamoMember"/>
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    <link:label id="lab_us-gaap_ConsolidationPolicyTextBlock_5f8c138a-bafd-4a1f-a581-68b7307bf679_terseLabel_en-US" xlink:label="lab_us-gaap_ConsolidationPolicyTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Principles of Consolidation</link:label>
    <link:label id="lab_us-gaap_ConsolidationPolicyTextBlock_label_en-US" xlink:label="lab_us-gaap_ConsolidationPolicyTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Consolidation, Policy [Policy Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ConsolidationPolicyTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_ConsolidationPolicyTextBlock"/>
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    <link:label id="lab_ecd_RestatementDateAxis_terseLabel_en-US" xlink:label="lab_ecd_RestatementDateAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Restatement Determination Date:</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_ecd_RestatementDateAxis" xlink:href="https://xbrl.sec.gov/ecd/2024/ecd-2024.xsd#ecd_RestatementDateAxis"/>
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    <link:label id="lab_codi_FairValueAssetsLiabilitiesQuantitativeInformationTable_a2699e7d-21ba-4d52-a828-353e3812f4c8_terseLabel_en-US" xlink:label="lab_codi_FairValueAssetsLiabilitiesQuantitativeInformationTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Fair Value Assets Liabilities Quantitative Information [Table]</link:label>
    <link:label id="lab_codi_FairValueAssetsLiabilitiesQuantitativeInformationTable_label_en-US" xlink:label="lab_codi_FairValueAssetsLiabilitiesQuantitativeInformationTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fair Value Assets Liabilities Quantitative Information [Table]</link:label>
    <link:label id="lab_codi_FairValueAssetsLiabilitiesQuantitativeInformationTable_documentation_en-US" xlink:label="lab_codi_FairValueAssetsLiabilitiesQuantitativeInformationTable" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Fair value assets liabilities quantitative information.</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_codi_FairValueAssetsLiabilitiesQuantitativeInformationTable" xlink:href="codi-20241231.xsd#codi_FairValueAssetsLiabilitiesQuantitativeInformationTable"/>
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    <link:label id="lab_codi_BusinessCombinationProvisionalInformationInitialAccountingIncompleteAdjustmentDeferredTaxLiabilities_8ef1bc24-81ee-4134-9456-bcb5646b3782_terseLabel_en-US" xlink:label="lab_codi_BusinessCombinationProvisionalInformationInitialAccountingIncompleteAdjustmentDeferredTaxLiabilities" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Business Combination, Provisional Information, Initial Accounting Incomplete, Adjustment, Deferred Tax Liabilities</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_codi_BusinessCombinationProvisionalInformationInitialAccountingIncompleteAdjustmentDeferredTaxLiabilities" xlink:href="codi-20241231.xsd#codi_BusinessCombinationProvisionalInformationInitialAccountingIncompleteAdjustmentDeferredTaxLiabilities"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_codi_BusinessCombinationProvisionalInformationInitialAccountingIncompleteAdjustmentDeferredTaxLiabilities" xlink:to="lab_codi_BusinessCombinationProvisionalInformationInitialAccountingIncompleteAdjustmentDeferredTaxLiabilities" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_Security12bTitle_97501052-2e9d-4df4-b78a-0eee0596a704_terseLabel_en-US" xlink:label="lab_dei_Security12bTitle" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Title of 12(b) Security</link:label>
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    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_Security12bTitle" xlink:to="lab_dei_Security12bTitle" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CommonStockValue_335d42fb-92b8-41de-9524-a96099fd5451_terseLabel_en-US" xlink:label="lab_us-gaap_CommonStockValue" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Trust common shares, no par value, 500,000 authorized; 76,135 shares issued and 75,236 shares outstanding at December 31, 2024 and 75,753 shares issued and 75,270 outstanding at December 31, 2023</link:label>
    <link:label id="lab_us-gaap_CommonStockValue_label_en-US" xlink:label="lab_us-gaap_CommonStockValue" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Common Stock, Value, Issued</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CommonStockValue" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_CommonStockValue"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CommonStockValue" xlink:to="lab_us-gaap_CommonStockValue" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_DocumentFinStmtErrorCorrectionFlag_3c99a87b-6bff-4756-9316-c7617196e89f_terseLabel_en-US" xlink:label="lab_dei_DocumentFinStmtErrorCorrectionFlag" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Document Financial Statement Error Correction [Flag]</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_dei_DocumentFinStmtErrorCorrectionFlag" xlink:href="https://xbrl.sec.gov/dei/2024/dei-2024.xsd#dei_DocumentFinStmtErrorCorrectionFlag"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_DocumentFinStmtErrorCorrectionFlag" xlink:to="lab_dei_DocumentFinStmtErrorCorrectionFlag" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FinanceLeaseInterestPaymentOnLiability_b5830c19-39b7-4990-9887-eadfb84b1071_terseLabel_en-US" xlink:label="lab_us-gaap_FinanceLeaseInterestPaymentOnLiability" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Finance Lease, Interest Payment on Liability</link:label>
    <link:label id="lab_us-gaap_FinanceLeaseInterestPaymentOnLiability_label_en-US" xlink:label="lab_us-gaap_FinanceLeaseInterestPaymentOnLiability" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Finance Lease, Interest Payment on Liability</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FinanceLeaseInterestPaymentOnLiability" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_FinanceLeaseInterestPaymentOnLiability"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FinanceLeaseInterestPaymentOnLiability" xlink:to="lab_us-gaap_FinanceLeaseInterestPaymentOnLiability" xlink:type="arc" order="1"/>
    <link:label id="lab_codi_PreferredSharesTaxRedemptionNoticePeriod_79394ee9-17c8-48a3-a191-b8013f76e18b_terseLabel_en-US" xlink:label="lab_codi_PreferredSharesTaxRedemptionNoticePeriod" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Preferred Shares Tax Redemption, Notice Period</link:label>
    <link:label id="lab_codi_PreferredSharesTaxRedemptionNoticePeriod_label_en-US" xlink:label="lab_codi_PreferredSharesTaxRedemptionNoticePeriod" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Preferred Shares Tax Redemption, Notice Period</link:label>
    <link:label id="lab_codi_PreferredSharesTaxRedemptionNoticePeriod_documentation_en-US" xlink:label="lab_codi_PreferredSharesTaxRedemptionNoticePeriod" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Preferred Shares Tax Redemption, Notice Period</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_codi_PreferredSharesTaxRedemptionNoticePeriod" xlink:href="codi-20241231.xsd#codi_PreferredSharesTaxRedemptionNoticePeriod"/>
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    <link:label id="lab_us-gaap_DefinedBenefitPlanExpectedFutureEmployerContributionsNextFiscalYear_a759cb81-8317-4c19-92f2-74efb354e421_terseLabel_en-US" xlink:label="lab_us-gaap_DefinedBenefitPlanExpectedFutureEmployerContributionsNextFiscalYear" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Defined benefit plan expected contribution by employer</link:label>
    <link:label id="lab_us-gaap_DefinedBenefitPlanExpectedFutureEmployerContributionsNextFiscalYear_label_en-US" xlink:label="lab_us-gaap_DefinedBenefitPlanExpectedFutureEmployerContributionsNextFiscalYear" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Defined Benefit Plan, Expected Future Employer Contributions, Next Fiscal Year</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DefinedBenefitPlanExpectedFutureEmployerContributionsNextFiscalYear" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_DefinedBenefitPlanExpectedFutureEmployerContributionsNextFiscalYear"/>
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    <link:label id="lab_us-gaap_AmortizationOfAcquisitionCosts_ec8fbb2e-8d0f-42fc-8cad-3ac2de13fe21_terseLabel_en-US" xlink:label="lab_us-gaap_AmortizationOfAcquisitionCosts" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Amortization of Acquisition Costs</link:label>
    <link:label id="lab_us-gaap_AmortizationOfAcquisitionCosts_label_en-US" xlink:label="lab_us-gaap_AmortizationOfAcquisitionCosts" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Amortization of Acquisition Costs</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AmortizationOfAcquisitionCosts" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_AmortizationOfAcquisitionCosts"/>
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    <link:label id="lab_us-gaap_FinanceLeaseLiabilityCurrentStatementOfFinancialPositionExtensibleList_b969166c-f22a-4294-aebb-5a4f2c507091_terseLabel_en-US" xlink:label="lab_us-gaap_FinanceLeaseLiabilityCurrentStatementOfFinancialPositionExtensibleList" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Finance Lease, Liability, Current, Statement of Financial Position [Extensible Enumeration]</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FinanceLeaseLiabilityCurrentStatementOfFinancialPositionExtensibleList" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_FinanceLeaseLiabilityCurrentStatementOfFinancialPositionExtensibleList"/>
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    <link:label id="lab_us-gaap_EffectiveIncomeTaxRateReconciliationStateAndLocalIncomeTaxes_c857b567-1d8e-4fa2-8e4f-da7c76b8b7a9_terseLabel_en-US" xlink:label="lab_us-gaap_EffectiveIncomeTaxRateReconciliationStateAndLocalIncomeTaxes" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">State income taxes (net of Federal benefits)</link:label>
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    <link:label id="lab_us-gaap_DeferredTaxAssetsOther_8b3639fc-59fc-4111-ba4f-30e86801c32f_terseLabel_en-US" xlink:label="lab_us-gaap_DeferredTaxAssetsOther" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Other</link:label>
    <link:label id="lab_us-gaap_DeferredTaxAssetsOther_label_en-US" xlink:label="lab_us-gaap_DeferredTaxAssetsOther" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Deferred Tax Assets, Other</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DeferredTaxAssetsOther" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_DeferredTaxAssetsOther"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DeferredTaxAssetsOther" xlink:to="lab_us-gaap_DeferredTaxAssetsOther" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FiniteLivedIntangibleAssetsLineItems_b8ace1b4-5915-47b1-8518-e6342ee51d10_terseLabel_en-US" xlink:label="lab_us-gaap_FiniteLivedIntangibleAssetsLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Finite-Lived Intangible Assets [Line Items]</link:label>
    <link:label id="lab_us-gaap_FiniteLivedIntangibleAssetsLineItems_label_en-US" xlink:label="lab_us-gaap_FiniteLivedIntangibleAssetsLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Finite-Lived Intangible Assets [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FiniteLivedIntangibleAssetsLineItems" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_FiniteLivedIntangibleAssetsLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FiniteLivedIntangibleAssetsLineItems" xlink:to="lab_us-gaap_FiniteLivedIntangibleAssetsLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_BusinessCombinationProvisionalInformationInitialAccountingIncompleteAdjustmentFinancialAssets_4ed3b95c-d307-4a9d-aefe-553e03f54bd6_terseLabel_en-US" xlink:label="lab_us-gaap_BusinessCombinationProvisionalInformationInitialAccountingIncompleteAdjustmentFinancialAssets" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Business Combination, Provisional Information, Initial Accounting Incomplete, Adjustment, Financial Assets</link:label>
    <link:label id="lab_us-gaap_BusinessCombinationProvisionalInformationInitialAccountingIncompleteAdjustmentFinancialAssets_label_en-US" xlink:label="lab_us-gaap_BusinessCombinationProvisionalInformationInitialAccountingIncompleteAdjustmentFinancialAssets" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Business Combination, Provisional Information, Initial Accounting Incomplete, Adjustment, Financial Assets</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_BusinessCombinationProvisionalInformationInitialAccountingIncompleteAdjustmentFinancialAssets" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_BusinessCombinationProvisionalInformationInitialAccountingIncompleteAdjustmentFinancialAssets"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_BusinessCombinationProvisionalInformationInitialAccountingIncompleteAdjustmentFinancialAssets" xlink:to="lab_us-gaap_BusinessCombinationProvisionalInformationInitialAccountingIncompleteAdjustmentFinancialAssets" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_NetCashProvidedByUsedInFinancingActivitiesAbstract_1e89d1a2-d4b5-4ab0-a3d3-042e93f66d2c_terseLabel_en-US" xlink:label="lab_us-gaap_NetCashProvidedByUsedInFinancingActivitiesAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Cash flows from financing activities:</link:label>
    <link:label id="lab_us-gaap_NetCashProvidedByUsedInFinancingActivitiesAbstract_label_en-US" xlink:label="lab_us-gaap_NetCashProvidedByUsedInFinancingActivitiesAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Net Cash Provided by (Used in) Financing Activities [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_NetCashProvidedByUsedInFinancingActivitiesAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_NetCashProvidedByUsedInFinancingActivitiesAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_NetCashProvidedByUsedInFinancingActivitiesAbstract" xlink:to="lab_us-gaap_NetCashProvidedByUsedInFinancingActivitiesAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DefinedBenefitPlanExpectedFutureBenefitPaymentsYearFive_e509bb21-8a58-479a-b2a7-f7cbaa289cd7_terseLabel_en-US" xlink:label="lab_us-gaap_DefinedBenefitPlanExpectedFutureBenefitPaymentsYearFive" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">2024</link:label>
    <link:label id="lab_us-gaap_DefinedBenefitPlanExpectedFutureBenefitPaymentsYearFive_label_en-US" xlink:label="lab_us-gaap_DefinedBenefitPlanExpectedFutureBenefitPaymentsYearFive" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Defined Benefit Plan, Expected Future Benefit Payment, Year Five</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DefinedBenefitPlanExpectedFutureBenefitPaymentsYearFive" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_DefinedBenefitPlanExpectedFutureBenefitPaymentsYearFive"/>
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    <link:label id="lab_us-gaap_PreferredStockValue_d2340041-858d-4c36-a227-a14f4dde14e9_terseLabel_en-US" xlink:label="lab_us-gaap_PreferredStockValue" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Preferred Stock, Value, Issued</link:label>
    <link:label id="lab_us-gaap_PreferredStockValue_label_en-US" xlink:label="lab_us-gaap_PreferredStockValue" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Preferred Stock, Value, Issued</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PreferredStockValue" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_PreferredStockValue"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PreferredStockValue" xlink:to="lab_us-gaap_PreferredStockValue" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OperatingLeaseLiabilityCurrentStatementOfFinancialPositionExtensibleList_b550b7f2-5708-47a5-8506-fb4225d33625_terseLabel_en-US" xlink:label="lab_us-gaap_OperatingLeaseLiabilityCurrentStatementOfFinancialPositionExtensibleList" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Operating Lease, Liability, Current, Statement of Financial Position [Extensible List]</link:label>
    <link:label id="lab_us-gaap_OperatingLeaseLiabilityCurrentStatementOfFinancialPositionExtensibleList_label_en-US" xlink:label="lab_us-gaap_OperatingLeaseLiabilityCurrentStatementOfFinancialPositionExtensibleList" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Operating Lease, Liability, Current, Statement of Financial Position [Extensible Enumeration]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OperatingLeaseLiabilityCurrentStatementOfFinancialPositionExtensibleList" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_OperatingLeaseLiabilityCurrentStatementOfFinancialPositionExtensibleList"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OperatingLeaseLiabilityCurrentStatementOfFinancialPositionExtensibleList" xlink:to="lab_us-gaap_OperatingLeaseLiabilityCurrentStatementOfFinancialPositionExtensibleList" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_InventoryFinishedGoods_08be84c1-bfb5-4cf2-bfac-7d3ab0addca2_terseLabel_en-US" xlink:label="lab_us-gaap_InventoryFinishedGoods" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Finished goods</link:label>
    <link:label id="lab_us-gaap_InventoryFinishedGoods_label_en-US" xlink:label="lab_us-gaap_InventoryFinishedGoods" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Inventory, Finished Goods, Gross</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_InventoryFinishedGoods" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_InventoryFinishedGoods"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_InventoryFinishedGoods" xlink:to="lab_us-gaap_InventoryFinishedGoods" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ReportingUnitDomain_b4ab90a3-026a-41af-9ac0-738d3c03532f_terseLabel_en-US" xlink:label="lab_us-gaap_ReportingUnitDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Reporting Unit [Domain]</link:label>
    <link:label id="lab_us-gaap_ReportingUnitDomain_label_en-US" xlink:label="lab_us-gaap_ReportingUnitDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Reporting Unit [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ReportingUnitDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_ReportingUnitDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ReportingUnitDomain" xlink:to="lab_us-gaap_ReportingUnitDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DeferredIncomeTaxLiabilities_3f25e689-1f10-4618-97a6-8778a5365b46_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_DeferredIncomeTaxLiabilities" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Recognized deferred tax liabilities</link:label>
    <link:label id="lab_us-gaap_DeferredIncomeTaxLiabilities_61e4c094-53e1-43f0-aeae-2d4cb685c9e5_negatedTotalLabel_en-US" xlink:label="lab_us-gaap_DeferredIncomeTaxLiabilities" xlink:role="http://www.xbrl.org/2009/role/negatedTotalLabel" xlink:type="resource" xml:lang="en-US">Total deferred tax liabilities</link:label>
    <link:label id="lab_us-gaap_DeferredIncomeTaxLiabilities_label_en-US" xlink:label="lab_us-gaap_DeferredIncomeTaxLiabilities" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Deferred Tax Liabilities, Gross</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DeferredIncomeTaxLiabilities" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_DeferredIncomeTaxLiabilities"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DeferredIncomeTaxLiabilities" xlink:to="lab_us-gaap_DeferredIncomeTaxLiabilities" xlink:type="arc" order="1"/>
    <link:label id="lab_codi_PercentageOwnershipFullyDilutedMember_6fa8a67a-33c1-42f4-9a2c-451ada957204_terseLabel_en-US" xlink:label="lab_codi_PercentageOwnershipFullyDilutedMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Fully Diluted</link:label>
    <link:label id="lab_codi_PercentageOwnershipFullyDilutedMember_label_en-US" xlink:label="lab_codi_PercentageOwnershipFullyDilutedMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Percentage Ownership Fully Diluted [Member]</link:label>
    <link:label id="lab_codi_PercentageOwnershipFullyDilutedMember_documentation_en-US" xlink:label="lab_codi_PercentageOwnershipFullyDilutedMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Percentage ownership fully diluted.</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_codi_PercentageOwnershipFullyDilutedMember" xlink:href="codi-20241231.xsd#codi_PercentageOwnershipFullyDilutedMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_codi_PercentageOwnershipFullyDilutedMember" xlink:to="lab_codi_PercentageOwnershipFullyDilutedMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ProceedsFromIssuanceOfCommonStock_ddcbb11e-c4a6-4022-81fb-afd848089c4b_terseLabel_en-US" xlink:label="lab_us-gaap_ProceedsFromIssuanceOfCommonStock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Proceeds from Issuance of Common Stock</link:label>
    <link:label id="lab_us-gaap_ProceedsFromIssuanceOfCommonStock_label_en-US" xlink:label="lab_us-gaap_ProceedsFromIssuanceOfCommonStock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Proceeds from Issuance of Common Stock</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ProceedsFromIssuanceOfCommonStock" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_ProceedsFromIssuanceOfCommonStock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ProceedsFromIssuanceOfCommonStock" xlink:to="lab_us-gaap_ProceedsFromIssuanceOfCommonStock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OperatingLeasePayments_c515ac10-3657-47fc-99f0-5e56de4a575e_terseLabel_en-US" xlink:label="lab_us-gaap_OperatingLeasePayments" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Operating Lease, Payments</link:label>
    <link:label id="lab_us-gaap_OperatingLeasePayments_label_en-US" xlink:label="lab_us-gaap_OperatingLeasePayments" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Operating Lease, Payments</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OperatingLeasePayments" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_OperatingLeasePayments"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OperatingLeasePayments" xlink:to="lab_us-gaap_OperatingLeasePayments" xlink:type="arc" order="1"/>
    <link:label id="lab_country_MX_a4eee878-3f00-4915-b9fc-58396641e8fe_terseLabel_en-US" xlink:label="lab_country_MX" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">MEXICO</link:label>
    <link:label id="lab_country_MX_label_en-US" xlink:label="lab_country_MX" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">MEXICO</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_country_MX" xlink:href="https://xbrl.sec.gov/country/2024/country-2024.xsd#country_MX"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_country_MX" xlink:to="lab_country_MX" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_AwardTmgMnpiDiscTextBlock_terseLabel_en-US" xlink:label="lab_ecd_AwardTmgMnpiDiscTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Award Timing MNPI Disclosure</link:label>
    <link:label id="lab_ecd_AwardTmgMnpiDiscTextBlock_label_en-US" xlink:label="lab_ecd_AwardTmgMnpiDiscTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Award Timing MNPI Disclosure [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_AwardTmgMnpiDiscTextBlock" xlink:href="https://xbrl.sec.gov/ecd/2024/ecd-2024.xsd#ecd_AwardTmgMnpiDiscTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_AwardTmgMnpiDiscTextBlock" xlink:to="lab_ecd_AwardTmgMnpiDiscTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedCurrentLiabilities_f8e21947-fc34-4d6d-bcd2-2242999d5771_terseLabel_en-US" xlink:label="lab_us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedCurrentLiabilities" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Current liabilities</link:label>
    <link:label id="lab_us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedCurrentLiabilities_label_en-US" xlink:label="lab_us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedCurrentLiabilities" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Business Combination, Recognized Identifiable Assets Acquired and Liabilities Assumed, Current Liabilities</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedCurrentLiabilities" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedCurrentLiabilities"/>
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    <link:label id="lab_srt_OwnershipDomain_5575005c-6704-40d0-a11d-f61f676039c1_terseLabel_en-US" xlink:label="lab_srt_OwnershipDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Ownership [Domain]</link:label>
    <link:label id="lab_srt_OwnershipDomain_label_en-US" xlink:label="lab_srt_OwnershipDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Ownership [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_srt_OwnershipDomain" xlink:href="https://xbrl.fasb.org/srt/2024/elts/srt-2024.xsd#srt_OwnershipDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_srt_OwnershipDomain" xlink:to="lab_srt_OwnershipDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_codi_UnobservableInputReconciliationBySupplementalPutLiabilityTableTextBlock_fbc6e861-bdf0-42cb-a47b-918144686a4d_terseLabel_en-US" xlink:label="lab_codi_UnobservableInputReconciliationBySupplementalPutLiabilityTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Reconciliations of Change in Carrying Value of Level 3 Supplemental Put Liability</link:label>
    <link:label id="lab_codi_UnobservableInputReconciliationBySupplementalPutLiabilityTableTextBlock_label_en-US" xlink:label="lab_codi_UnobservableInputReconciliationBySupplementalPutLiabilityTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Unobservable Input Reconciliation By Supplemental Put Liability Table [Text Block]</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_codi_UnobservableInputReconciliationBySupplementalPutLiabilityTableTextBlock" xlink:href="codi-20241231.xsd#codi_UnobservableInputReconciliationBySupplementalPutLiabilityTableTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_codi_UnobservableInputReconciliationBySupplementalPutLiabilityTableTextBlock" xlink:to="lab_codi_UnobservableInputReconciliationBySupplementalPutLiabilityTableTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_codi_ScheduleOfOtherRelatedPartyTransactionsTable_f97c4979-7da8-4ef0-9e69-cbfc909c49ee_terseLabel_en-US" xlink:label="lab_codi_ScheduleOfOtherRelatedPartyTransactionsTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Other Related Party Transactions [Table]</link:label>
    <link:label id="lab_codi_ScheduleOfOtherRelatedPartyTransactionsTable_label_en-US" xlink:label="lab_codi_ScheduleOfOtherRelatedPartyTransactionsTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Schedule Of Other Related Party Transactions [Table]</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_codi_ScheduleOfOtherRelatedPartyTransactionsTable" xlink:href="codi-20241231.xsd#codi_ScheduleOfOtherRelatedPartyTransactionsTable"/>
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    <link:label id="lab_ecd_AggtPnsnAdjsSvcCstMember_terseLabel_en-US" xlink:label="lab_ecd_AggtPnsnAdjsSvcCstMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Aggregate Pension Adjustments Service Cost</link:label>
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    <link:label id="lab_us-gaap_DefinedBenefitPlanWeightedAverageAssetAllocations_711e97ee-b559-4e59-aff8-ee56a8cc5028_terseLabel_en-US" xlink:label="lab_us-gaap_DefinedBenefitPlanWeightedAverageAssetAllocations" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Allocation of pension plan assets</link:label>
    <link:label id="lab_us-gaap_DefinedBenefitPlanWeightedAverageAssetAllocations_label_en-US" xlink:label="lab_us-gaap_DefinedBenefitPlanWeightedAverageAssetAllocations" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Defined Benefit Plan, Plan Assets, Actual Allocation, Percentage</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DefinedBenefitPlanWeightedAverageAssetAllocations" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_DefinedBenefitPlanWeightedAverageAssetAllocations"/>
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    <link:label id="lab_us-gaap_ScheduleOfGoodwillTable_0a4a327e-6ade-424f-b6fb-1cb0c6a71dee_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfGoodwillTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Goodwill [Table]</link:label>
    <link:label id="lab_us-gaap_ScheduleOfGoodwillTable_label_en-US" xlink:label="lab_us-gaap_ScheduleOfGoodwillTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Goodwill [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfGoodwillTable" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_ScheduleOfGoodwillTable"/>
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    <link:label id="lab_us-gaap_IndefiniteLivedTradeNames_b4036261-0915-4bbb-8928-449e2d28d95f_terseLabel_en-US" xlink:label="lab_us-gaap_IndefiniteLivedTradeNames" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Trade names, not subject to amortization</link:label>
    <link:label id="lab_us-gaap_IndefiniteLivedTradeNames_label_en-US" xlink:label="lab_us-gaap_IndefiniteLivedTradeNames" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Indefinite-Lived Trade Names</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IndefiniteLivedTradeNames" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_IndefiniteLivedTradeNames"/>
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    <link:label id="lab_us-gaap_PropertyPlantAndEquipmentPolicyTextBlock_efb9aff8-1121-454e-9bf6-e249788e72fe_terseLabel_en-US" xlink:label="lab_us-gaap_PropertyPlantAndEquipmentPolicyTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Property, Plant and Equipment</link:label>
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    <link:label id="lab_us-gaap_DeferredTaxLiabilitiesGoodwillAndIntangibleAssetsIntangibleAssets_774d6dbd-117b-4376-a330-09974d2ce92c_negatedLabel_en-US" xlink:label="lab_us-gaap_DeferredTaxLiabilitiesGoodwillAndIntangibleAssetsIntangibleAssets" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:type="resource" xml:lang="en-US">Intangible assets</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DeferredTaxLiabilitiesGoodwillAndIntangibleAssetsIntangibleAssets" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_DeferredTaxLiabilitiesGoodwillAndIntangibleAssetsIntangibleAssets"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DeferredTaxLiabilitiesGoodwillAndIntangibleAssetsIntangibleAssets" xlink:to="lab_us-gaap_DeferredTaxLiabilitiesGoodwillAndIntangibleAssetsIntangibleAssets" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LiabilitiesCurrent_69800538-c4d8-4962-bdc3-534add5c3fa9_totalLabel_en-US" xlink:label="lab_us-gaap_LiabilitiesCurrent" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Total current liabilities</link:label>
    <link:label id="lab_us-gaap_LiabilitiesCurrent_label_en-US" xlink:label="lab_us-gaap_LiabilitiesCurrent" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Liabilities, Current</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LiabilitiesCurrent" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_LiabilitiesCurrent"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LiabilitiesCurrent" xlink:to="lab_us-gaap_LiabilitiesCurrent" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_EmployeeServiceShareBasedCompensationNonvestedAwardsTotalCompensationCostNotYetRecognizedStockOptions_2bc39f52-4b9b-4b63-b355-01841b95956c_terseLabel_en-US" xlink:label="lab_us-gaap_EmployeeServiceShareBasedCompensationNonvestedAwardsTotalCompensationCostNotYetRecognizedStockOptions" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Stock compensation expense in future years for unvested options</link:label>
    <link:label id="lab_us-gaap_EmployeeServiceShareBasedCompensationNonvestedAwardsTotalCompensationCostNotYetRecognizedStockOptions_label_en-US" xlink:label="lab_us-gaap_EmployeeServiceShareBasedCompensationNonvestedAwardsTotalCompensationCostNotYetRecognizedStockOptions" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Share-Based Payment Arrangement, Nonvested Award, Option, Cost Not yet Recognized, Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_EmployeeServiceShareBasedCompensationNonvestedAwardsTotalCompensationCostNotYetRecognizedStockOptions" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_EmployeeServiceShareBasedCompensationNonvestedAwardsTotalCompensationCostNotYetRecognizedStockOptions"/>
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    <link:label id="lab_us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseNextTwelveMonths_70525266-b297-4a08-8d0a-048d0532e156_terseLabel_en-US" xlink:label="lab_us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseNextTwelveMonths" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">2020</link:label>
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    <link:label id="lab_us-gaap_ReconciliationOfOperatingProfitLossFromSegmentsToConsolidatedAbstract_6af600ce-930e-44f1-a869-115a5814a428_terseLabel_en-US" xlink:label="lab_us-gaap_ReconciliationOfOperatingProfitLossFromSegmentsToConsolidatedAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Reconciliation of Operating Profit (Loss) from Segments to Consolidated [Abstract]</link:label>
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    <link:label id="lab_us-gaap_BusinessCombinationsPolicy_7ec92073-ba30-4ff5-bc74-28745c2fa212_terseLabel_en-US" xlink:label="lab_us-gaap_BusinessCombinationsPolicy" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Business Combinations</link:label>
    <link:label id="lab_us-gaap_BusinessCombinationsPolicy_label_en-US" xlink:label="lab_us-gaap_BusinessCombinationsPolicy" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Business Combinations Policy [Policy Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_BusinessCombinationsPolicy" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_BusinessCombinationsPolicy"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_BusinessCombinationsPolicy" xlink:to="lab_us-gaap_BusinessCombinationsPolicy" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_NoncontrollingInterestDecreaseFromDeconsolidation_c114d20a-2414-4f7f-a874-3f6ef73900c7_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_NoncontrollingInterestDecreaseFromDeconsolidation" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Noncontrolling Interest, Decrease from Deconsolidation</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_NoncontrollingInterestDecreaseFromDeconsolidation" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_NoncontrollingInterestDecreaseFromDeconsolidation"/>
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    <link:label id="lab_codi_OwnershipInterest_13a1e87e-9a53-470b-bf74-ce49861ed579_terseLabel_en-US" xlink:label="lab_codi_OwnershipInterest" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Ownership Interest</link:label>
    <link:label id="lab_codi_OwnershipInterest_label_en-US" xlink:label="lab_codi_OwnershipInterest" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Ownership Interest</link:label>
    <link:label id="lab_codi_OwnershipInterest_documentation_en-US" xlink:label="lab_codi_OwnershipInterest" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Ownership Interest</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_codi_OwnershipInterest" xlink:href="codi-20241231.xsd#codi_OwnershipInterest"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_codi_OwnershipInterest" xlink:to="lab_codi_OwnershipInterest" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_EntityAddressCityOrTown_3729f6e7-74c5-4d5d-849d-ef9684efe660_terseLabel_en-US" xlink:label="lab_dei_EntityAddressCityOrTown" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Entity Address, City or Town</link:label>
    <link:label id="lab_dei_EntityAddressCityOrTown_label_en-US" xlink:label="lab_dei_EntityAddressCityOrTown" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Entity Address, City or Town</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityAddressCityOrTown" xlink:href="https://xbrl.sec.gov/dei/2024/dei-2024.xsd#dei_EntityAddressCityOrTown"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_EntityAddressCityOrTown" xlink:to="lab_dei_EntityAddressCityOrTown" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_BusinessAcquisitionProFormaInformationNonrecurringAdjustmentLineItems_beae5c46-53f7-4c43-bd13-6f6ee0f6ffad_terseLabel_en-US" xlink:label="lab_us-gaap_BusinessAcquisitionProFormaInformationNonrecurringAdjustmentLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Business Acquisition, Pro Forma Information, Nonrecurring Adjustment [Line Items]</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_BusinessAcquisitionProFormaInformationNonrecurringAdjustmentLineItems" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_BusinessAcquisitionProFormaInformationNonrecurringAdjustmentLineItems"/>
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    <link:label id="lab_us-gaap_LiabilitiesOfDisposalGroupIncludingDiscontinuedOperationNoncurrent_fca6fefc-cf9c-4819-a48e-8a06ea2711dd_terseLabel_en-US" xlink:label="lab_us-gaap_LiabilitiesOfDisposalGroupIncludingDiscontinuedOperationNoncurrent" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Disposal Group, Including Discontinued Operation, Liabilities, Noncurrent</link:label>
    <link:label id="lab_us-gaap_LiabilitiesOfDisposalGroupIncludingDiscontinuedOperationNoncurrent_label_en-US" xlink:label="lab_us-gaap_LiabilitiesOfDisposalGroupIncludingDiscontinuedOperationNoncurrent" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Disposal Group, Including Discontinued Operation, Liabilities, Noncurrent</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LiabilitiesOfDisposalGroupIncludingDiscontinuedOperationNoncurrent" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_LiabilitiesOfDisposalGroupIncludingDiscontinuedOperationNoncurrent"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LiabilitiesOfDisposalGroupIncludingDiscontinuedOperationNoncurrent" xlink:to="lab_us-gaap_LiabilitiesOfDisposalGroupIncludingDiscontinuedOperationNoncurrent" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AllocatedShareBasedCompensationExpense_7495f2bb-2853-40d7-9b3e-4c9275781af2_terseLabel_en-US" xlink:label="lab_us-gaap_AllocatedShareBasedCompensationExpense" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Share-based Payment Arrangement, Expense</link:label>
    <link:label id="lab_us-gaap_AllocatedShareBasedCompensationExpense_label_en-US" xlink:label="lab_us-gaap_AllocatedShareBasedCompensationExpense" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Share-Based Payment Arrangement, Expense</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AllocatedShareBasedCompensationExpense" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_AllocatedShareBasedCompensationExpense"/>
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    <link:label id="lab_us-gaap_DisposalGroupsIncludingDiscontinuedOperationsDisclosureTextBlock_6ce890e0-5c5c-482b-a810-1a904a08a661_terseLabel_en-US" xlink:label="lab_us-gaap_DisposalGroupsIncludingDiscontinuedOperationsDisclosureTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Discontinued Operations</link:label>
    <link:label id="lab_us-gaap_DisposalGroupsIncludingDiscontinuedOperationsDisclosureTextBlock_label_en-US" xlink:label="lab_us-gaap_DisposalGroupsIncludingDiscontinuedOperationsDisclosureTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Disposal Groups, Including Discontinued Operations, Disclosure [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DisposalGroupsIncludingDiscontinuedOperationsDisclosureTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_DisposalGroupsIncludingDiscontinuedOperationsDisclosureTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DisposalGroupsIncludingDiscontinuedOperationsDisclosureTextBlock" xlink:to="lab_us-gaap_DisposalGroupsIncludingDiscontinuedOperationsDisclosureTextBlock" xlink:type="arc" order="1"/>
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    <link:label id="lab_ecd_DvddsOrOthrErngsPdOnEqtyAwrdsNtOthrwsRflctdInTtlCompForCvrdYrMember_terseLabel_en-US" xlink:label="lab_ecd_DvddsOrOthrErngsPdOnEqtyAwrdsNtOthrwsRflctdInTtlCompForCvrdYrMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Dividends or Other Earnings Paid on Equity Awards not Otherwise Reflected in Total Compensation for Covered Year</link:label>
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    <link:label id="lab_us-gaap_ForeignCountryMember_02d798fc-d01e-49e6-9dae-46f3788ac3cd_terseLabel_en-US" xlink:label="lab_us-gaap_ForeignCountryMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Foreign Tax Jurisdiction</link:label>
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    <link:label id="lab_codi_NonUnitedStatesMember_documentation_en-US" xlink:label="lab_codi_NonUnitedStatesMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Non United States.</link:label>
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    <link:label id="lab_us-gaap_DeferredTaxLiabilitiesLeasingArrangements_2627c51b-e703-48c2-897c-b0a518e9e9ef_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_DeferredTaxLiabilitiesLeasingArrangements" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Deferred Tax Liabilities, Leasing Arrangements</link:label>
    <link:label id="lab_us-gaap_DeferredTaxLiabilitiesLeasingArrangements_label_en-US" xlink:label="lab_us-gaap_DeferredTaxLiabilitiesLeasingArrangements" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Deferred Tax Liabilities, Leasing Arrangements</link:label>
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    <link:label id="lab_codi_LesseeOperatingAndFinancingLeaseLiabilityPaymentsDue_e8608572-dad6-4cb4-9855-510fdbb93d86_terseLabel_en-US" xlink:label="lab_codi_LesseeOperatingAndFinancingLeaseLiabilityPaymentsDue" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Total undiscounted lease payments</link:label>
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    <link:label id="lab_codi_LesseeOperatingAndFinancingLeaseLiabilityPaymentsDue_documentation_en-US" xlink:label="lab_codi_LesseeOperatingAndFinancingLeaseLiabilityPaymentsDue" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Lessee Operating and Financing Lease Liability Payments Due</link:label>
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    <link:label id="lab_us-gaap_SeriesBPreferredStockMember_6ffdb2e6-11b6-415a-8ccd-16898d347a22_terseLabel_en-US" xlink:label="lab_us-gaap_SeriesBPreferredStockMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Series B Preferred Stock [Member]</link:label>
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    <link:label id="lab_us-gaap_RevenueFromContractWithCustomerTextBlock_5bf961ed-727e-4b89-84e4-f91b60c49be6_terseLabel_en-US" xlink:label="lab_us-gaap_RevenueFromContractWithCustomerTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Revenue from Contract with Customer [Text Block]</link:label>
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    <link:label id="lab_us-gaap_TreasuryStockValueAcquiredCostMethod_a46bca09-f680-4533-a14a-88c4e25d00d4_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_TreasuryStockValueAcquiredCostMethod" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Stock Repurchased During Period, Value</link:label>
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    <link:label id="lab_us-gaap_DisposalGroupIncludingDiscontinuedOperationDeferredTaxLiabilities_2b06816f-5b46-4a3d-8911-c0485b88e219_terseLabel_en-US" xlink:label="lab_us-gaap_DisposalGroupIncludingDiscontinuedOperationDeferredTaxLiabilities" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Disposal Group, Including Discontinued Operation, Deferred Tax Liabilities</link:label>
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    <link:label id="lab_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearThree_49b18069-3acd-4f12-8665-c9f4b2130295_terseLabel_en-US" xlink:label="lab_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearThree" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">2022</link:label>
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    <link:label id="lab_us-gaap_ValuationAllowanceTable_9a1d5241-2ee4-4a95-a491-7c8882f17019_terseLabel_en-US" xlink:label="lab_us-gaap_ValuationAllowanceTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Deferred Tax Asset, Valuation Allowance [Table]</link:label>
    <link:label id="lab_us-gaap_ValuationAllowanceTable_label_en-US" xlink:label="lab_us-gaap_ValuationAllowanceTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Deferred Tax Asset, Valuation Allowance [Table]</link:label>
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