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    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OtherNoncurrentAssetsMember" xlink:to="lab_us-gaap_OtherNoncurrentAssetsMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LeasesAbstract_9a93e084-8670-4f8d-bc77-396fe162fbc2_terseLabel_en-US" xlink:label="lab_us-gaap_LeasesAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Leases [Abstract]</link:label>
    <link:label id="lab_us-gaap_LeasesAbstract_label_en-US" xlink:label="lab_us-gaap_LeasesAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Leases [Abstract]</link:label>
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    <link:label id="lab_codi_DistributionExpensePreferredShareholders_documentation_en-US" xlink:label="lab_codi_DistributionExpensePreferredShareholders" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Distribution Expense, Preferred Shareholders</link:label>
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    <link:label id="lab_us-gaap_AcquiredFiniteLivedIntangibleAssetsLineItems_6140f87f-8122-4732-9d8a-96d0e5caf1c0_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">Intangible Asset, Acquired, Finite-Lived [Line Items]</link:label>
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    <link:label id="lab_us-gaap_StatementOperatingActivitiesSegmentAxis_901ab6cc-4cb8-40c8-8efa-19865a85cdd4_terseLabel_en-US" xlink:label="lab_us-gaap_StatementOperatingActivitiesSegmentAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Operating Activities [Axis]</link:label>
    <link:label id="lab_us-gaap_StatementOperatingActivitiesSegmentAxis_label_en-US" xlink:label="lab_us-gaap_StatementOperatingActivitiesSegmentAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Operating Activities [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_StatementOperatingActivitiesSegmentAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_StatementOperatingActivitiesSegmentAxis"/>
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    <link:label id="lab_codi_AltorMember_7f4bd78a-8dd1-42e1-9dd8-548f7c199950_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>
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    <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>
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    <link:label id="lab_us-gaap_BusinessCombinationConsiderationTransferredLiabilitiesIncurred_dc3df27e-8a6d-4754-9366-35bab20b0f36_terseLabel_en-US" xlink:label="lab_us-gaap_BusinessCombinationConsiderationTransferredLiabilitiesIncurred" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Business Combination, Consideration Transferred, Liabilities Incurred</link:label>
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    <link:label id="lab_us-gaap_InterestIncomeExpenseNonoperatingNet_b365172d-25d2-4b84-a3c9-4630935c1eb5_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>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_InterestIncomeExpenseNonoperatingNet" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_InterestIncomeExpenseNonoperatingNet"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_InterestIncomeExpenseNonoperatingNet" xlink:to="lab_us-gaap_InterestIncomeExpenseNonoperatingNet" xlink:type="arc" order="1"/>
    <link:label id="lab_codi_LeaseLiability_6b9d27a0-789c-432a-ab51-a7fa9205a9d3_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-20250331.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_GoodwillLineItems_8d22d314-f702-42cd-8785-e31097a101ea_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/2025/elts/us-gaap-2025.xsd#us-gaap_GoodwillLineItems"/>
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    <link:label id="lab_us-gaap_FederalFundsEffectiveSwapRateMember_5a0201c9-d8f9-43ae-97f6-bde2fe3a909e_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">Fed Funds Effective Rate Overnight Index Swap Rate</link:label>
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    <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/2025/elts/us-gaap-2025.xsd#us-gaap_FairValueByMeasurementBasisAxis"/>
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    <link:label id="lab_us-gaap_RelatedPartyTransactionsDisclosureTextBlock_5d08c208-f543-4483-867d-cb29386d5d6a_terseLabel_en-US" xlink:label="lab_us-gaap_RelatedPartyTransactionsDisclosureTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Related Party Transactions</link:label>
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    <link:label id="lab_codi_OwnershipPercentageOfNoncontrollingShareholders_5fb9254f-b4f5-4d3c-a950-a5f418624098_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>
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    <link:label id="lab_us-gaap_IncomeLossFromDiscontinuedOperationsNetOfTaxAttributableToNoncontrollingInterest_33541ede-230d-416d-b1cd-a95b882c2ebe_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 loss from discontinued operations attributable to noncontrolling interest</link:label>
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    <link:label id="lab_us-gaap_RevenueFromContractWithCustomerTextBlock_5a10aef8-34bd-43d3-9e57-eed827f930e0_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</link:label>
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    <link:label id="lab_us-gaap_DisposalGroupIncludingDiscontinuedOperationCash_7278b620-e4e7-4488-a1c7-df0c30aecca4_terseLabel_en-US" xlink:label="lab_us-gaap_DisposalGroupIncludingDiscontinuedOperationCash" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Disposal Group, Including Discontinued Operation, Cash</link:label>
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    <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>
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    <link:label id="lab_us-gaap_ScheduleOfPropertyPlantAndEquipmentTable_5506d92a-d224-4acb-8de3-b9fcbe0bd6ba_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>
    <link:label id="lab_us-gaap_ScheduleOfPropertyPlantAndEquipmentTable_label_en-US" xlink:label="lab_us-gaap_ScheduleOfPropertyPlantAndEquipmentTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Property, Plant and Equipment [Table]</link:label>
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    <link:label id="lab_us-gaap_AssetImpairmentCharges_0e4d3b8c-861c-4274-8fb2-650c3f1f6f5a_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_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>
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    <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/2025/elts/us-gaap-2025.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_ExtinguishmentOfDebtAxis_51067290-5e81-450b-8bea-1b0f6b0cf973_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>
    <link:label id="lab_us-gaap_ExtinguishmentOfDebtAxis_label_en-US" xlink:label="lab_us-gaap_ExtinguishmentOfDebtAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Extinguishment of Debt [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ExtinguishmentOfDebtAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ExtinguishmentOfDebtAxis"/>
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    <link:label id="lab_codi_LineOfCreditFacilityAdditionalBorrowing_label_en-US" xlink:label="lab_codi_LineOfCreditFacilityAdditionalBorrowing" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Line of Credit Facility, Additional Borrowing</link:label>
    <link:label id="lab_codi_LineOfCreditFacilityAdditionalBorrowing_documentation_en-US" xlink:label="lab_codi_LineOfCreditFacilityAdditionalBorrowing" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Line of Credit Facility, Additional Borrowing</link:label>
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    <link:label id="lab_us-gaap_StockIssuedDuringPeriodSharesNewIssues_28d9e8dd-4aba-41c1-b472-ebff89736a1b_terseLabel_en-US" xlink:label="lab_us-gaap_StockIssuedDuringPeriodSharesNewIssues" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Stock Issued During Period, Shares, New Issues</link:label>
    <link:label id="lab_us-gaap_StockIssuedDuringPeriodSharesNewIssues_label_en-US" xlink:label="lab_us-gaap_StockIssuedDuringPeriodSharesNewIssues" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Stock Issued During Period, Shares, New Issues</link:label>
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    <link:label id="lab_us-gaap_AssetsCurrentAbstract_b9d3b1f9-6ef0-47a5-ba7c-a8ccbdbfb70e_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>
    <link:label id="lab_us-gaap_AssetsCurrentAbstract_label_en-US" xlink:label="lab_us-gaap_AssetsCurrentAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Assets, Current [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AssetsCurrentAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_AssetsCurrentAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AssetsCurrentAbstract" xlink:to="lab_us-gaap_AssetsCurrentAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LiabilitiesAndStockholdersEquity_61a96bf1-e0c5-4454-8933-4a298d525379_totalLabel_en-US" xlink:label="lab_us-gaap_LiabilitiesAndStockholdersEquity" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Total liabilities and stockholders&#8217; equity</link:label>
    <link:label id="lab_us-gaap_LiabilitiesAndStockholdersEquity_label_en-US" xlink:label="lab_us-gaap_LiabilitiesAndStockholdersEquity" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Liabilities and Equity</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LiabilitiesAndStockholdersEquity" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_LiabilitiesAndStockholdersEquity"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LiabilitiesAndStockholdersEquity" xlink:to="lab_us-gaap_LiabilitiesAndStockholdersEquity" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_MinorityInterestLineItems_30472072-c8b3-454b-8e20-f496a8f2edb0_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/2025/elts/us-gaap-2025.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"/>
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    <link:label id="lab_us-gaap_LiabilitiesAndStockholdersEquityAbstract_f700b168-d054-45fc-adea-36380bf047d2_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>
    <link:label id="lab_us-gaap_LiabilitiesAndStockholdersEquityAbstract_label_en-US" xlink:label="lab_us-gaap_LiabilitiesAndStockholdersEquityAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Liabilities and Equity [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LiabilitiesAndStockholdersEquityAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_LiabilitiesAndStockholdersEquityAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LiabilitiesAndStockholdersEquityAbstract" xlink:to="lab_us-gaap_LiabilitiesAndStockholdersEquityAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_CoverAbstract_ea9ff980-6715-4364-8778-a1eebe1b83e8_terseLabel_en-US" xlink:label="lab_dei_CoverAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Cover [Abstract]</link:label>
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    <link:label id="lab_us-gaap_PortionAtFairValueFairValueDisclosureMember_aa6bdf92-eeea-42d7-953c-a20a7a96aba2_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/2025/elts/us-gaap-2025.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_DisposalGroupsIncludingDiscontinuedOperationsDisclosureTextBlock_8bb574b6-3acd-46e2-bf5b-3579e5731d48_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">Disposal Groups, Including Discontinued Operations, Disclosure [Text Block]</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/2025/elts/us-gaap-2025.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"/>
    <link:label id="lab_srt_MaximumMember_eb7010be-b034-4f23-af14-b28033a98720_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/2025/elts/srt-2025.xsd#srt_MaximumMember"/>
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    <link:label id="lab_us-gaap_ScheduleOfEquityMethodInvestmentsTable_060de84d-1e06-4884-91d5-0df16a594d9d_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfEquityMethodInvestmentsTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Equity Method Investments [Table]</link:label>
    <link:label id="lab_us-gaap_ScheduleOfEquityMethodInvestmentsTable_label_en-US" xlink:label="lab_us-gaap_ScheduleOfEquityMethodInvestmentsTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Equity Method Investment [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfEquityMethodInvestmentsTable" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ScheduleOfEquityMethodInvestmentsTable"/>
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    <link:label id="lab_us-gaap_NetIncomeLossAttributableToNoncontrollingInterest_c224c1cd-18b2-4eed-84cb-90253fb51883_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 loss attributable to noncontrolling interests</link:label>
    <link:label id="lab_us-gaap_NetIncomeLossAttributableToNoncontrollingInterest_label_en-US" xlink:label="lab_us-gaap_NetIncomeLossAttributableToNoncontrollingInterest" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Net Income (Loss) Attributable to Noncontrolling Interest</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_NetIncomeLossAttributableToNoncontrollingInterest" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_NetIncomeLossAttributableToNoncontrollingInterest"/>
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    <link:label id="lab_us-gaap_GuaranteesAbstract_d0a36154-268e-4edf-b192-77a93729fc59_terseLabel_en-US" xlink:label="lab_us-gaap_GuaranteesAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Guarantees [Abstract]</link:label>
    <link:label id="lab_us-gaap_GuaranteesAbstract_label_en-US" xlink:label="lab_us-gaap_GuaranteesAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Guarantees [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_GuaranteesAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_GuaranteesAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_GuaranteesAbstract" xlink:to="lab_us-gaap_GuaranteesAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AccountingPoliciesAbstract_816cc78f-8e63-4594-8d3b-8107d09a1429_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>
    <link:label id="lab_us-gaap_AccountingPoliciesAbstract_label_en-US" xlink:label="lab_us-gaap_AccountingPoliciesAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Accounting Policies [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AccountingPoliciesAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_AccountingPoliciesAbstract"/>
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    <link:label id="lab_us-gaap_FiniteLivedIntangibleAssetsNet_59a14c45-4c39-4e25-85cb-039b795d6a82_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">Finite-Lived Intangible Assets, Net</link:label>
    <link:label id="lab_us-gaap_FiniteLivedIntangibleAssetsNet_label_en-US" xlink:label="lab_us-gaap_FiniteLivedIntangibleAssetsNet" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Finite-Lived Intangible Assets, Net</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FiniteLivedIntangibleAssetsNet" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FiniteLivedIntangibleAssetsNet"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FiniteLivedIntangibleAssetsNet" xlink:to="lab_us-gaap_FiniteLivedIntangibleAssetsNet" xlink:type="arc" order="1"/>
    <link:label id="lab_codi_FixedPIKPayment_019b2351-fb68-7bc9-b4b1-00ebd7ee7003_terseLabel_en-US" xlink:label="lab_codi_FixedPIKPayment" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Fixed PIK payment</link:label>
    <link:label id="lab_codi_FixedPIKPayment_label_en-US" xlink:label="lab_codi_FixedPIKPayment" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fixed PIK payment</link:label>
    <link:label id="lab_codi_FixedPIKPayment_documentation_en-US" xlink:label="lab_codi_FixedPIKPayment" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Fixed PIK payment</link:label>
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    <link:label id="lab_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearFour_977756ea-5969-495d-b5aa-324a7edb1eea_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">2022</link:label>
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    <link:label id="lab_us-gaap_ProductWarrantyAccrualWarrantiesIssued_b564a8ab-e63f-4e52-9890-9cd5ed4542b8_terseLabel_en-US" xlink:label="lab_us-gaap_ProductWarrantyAccrualWarrantiesIssued" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Provision for warranties issued during the period</link:label>
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    <link:label id="lab_us-gaap_NetCashProvidedByUsedInOperatingActivitiesAbstract_770c0ea1-a31d-4e16-b462-648d20a22663_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>
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    <link:label id="lab_us-gaap_BusinessCombinationConsiderationTransferred1_6b6a5798-0817-4dca-baf6-39d50d9a4768_terseLabel_en-US" xlink:label="lab_us-gaap_BusinessCombinationConsiderationTransferred1" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Business Combination, Consideration Transferred</link:label>
    <link:label id="lab_us-gaap_BusinessCombinationConsiderationTransferred1_label_en-US" xlink:label="lab_us-gaap_BusinessCombinationConsiderationTransferred1" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Business Combination, Consideration Transferred</link:label>
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    <link:label id="lab_us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseYearFour_36ebd747-63ea-476b-bf1a-47196a9d0065_terseLabel_en-US" xlink:label="lab_us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseYearFour" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">2025</link:label>
    <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/2025/elts/us-gaap-2025.xsd#us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseYearFour"/>
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    <link:label id="lab_dei_EntityEmergingGrowthCompany_12097a25-4e49-4152-9d2b-5dc8086eaa58_terseLabel_en-US" xlink:label="lab_dei_EntityEmergingGrowthCompany" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Entity Emerging Growth Company</link:label>
    <link:label id="lab_dei_EntityEmergingGrowthCompany_label_en-US" xlink:label="lab_dei_EntityEmergingGrowthCompany" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Entity Emerging Growth Company</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityEmergingGrowthCompany" xlink:href="https://xbrl.sec.gov/dei/2025/dei-2025.xsd#dei_EntityEmergingGrowthCompany"/>
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    <link:label id="lab_us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInYearThree_18cfd7b3-7366-46dd-bfea-8d6d8a9c719f_terseLabel_en-US" xlink:label="lab_us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInYearThree" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Long-Term Debt, Maturity, Year Three</link:label>
    <link:label id="lab_us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInYearThree_label_en-US" xlink:label="lab_us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInYearThree" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Long-Term Debt, Maturity, Year Three</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInYearThree" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInYearThree"/>
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    <link:label id="lab_us-gaap_ImpairmentOfLongLivedAssetsHeldForUse_019b17d6-23e3-749a-aad1-5e00d1b6044c_terseLabel_en-US" xlink:label="lab_us-gaap_ImpairmentOfLongLivedAssetsHeldForUse" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Impairment, Long-Lived Asset, Held-for-Use</link:label>
    <link:label id="lab_us-gaap_ImpairmentOfLongLivedAssetsHeldForUse_label_en-US" xlink:label="lab_us-gaap_ImpairmentOfLongLivedAssetsHeldForUse" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Impairment, Long-Lived Asset, Held-for-Use</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ImpairmentOfLongLivedAssetsHeldForUse" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ImpairmentOfLongLivedAssetsHeldForUse"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ImpairmentOfLongLivedAssetsHeldForUse" xlink:to="lab_us-gaap_ImpairmentOfLongLivedAssetsHeldForUse" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FinanceLeaseLiabilityPaymentsDueNextTwelveMonths_93eef64a-9c9b-499e-b2d5-b94fdfcd9874_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/2025/elts/us-gaap-2025.xsd#us-gaap_FinanceLeaseLiabilityPaymentsDueNextTwelveMonths"/>
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    <link:label id="lab_us-gaap_CommonStockDividendsPerShareDeclared_362efaf3-49ea-4cf3-9b06-bf90b01bc5be_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 distributions declared per share (refer to Note J) (usd per share)</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/2025/elts/us-gaap-2025.xsd#us-gaap_CommonStockDividendsPerShareDeclared"/>
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    <link:label id="lab_dei_EntityCommonStockSharesOutstanding_3c65594b-4ca8-4cc1-9521-6fbf00e8ed59_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/2025/dei-2025.xsd#dei_EntityCommonStockSharesOutstanding"/>
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    <link:label id="lab_us-gaap_FinanceLeaseWeightedAverageRemainingLeaseTerm1_a6eecf87-60a2-413e-91e6-6555c8f5d64b_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/2025/elts/us-gaap-2025.xsd#us-gaap_FinanceLeaseWeightedAverageRemainingLeaseTerm1"/>
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    <link:label id="lab_us-gaap_RightOfUseAssetObtainedInExchangeForOperatingLeaseLiability_b2076a5f-42c8-4ee8-a2d5-be15719b732d_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:loc xlink:type="locator" xlink:label="loc_us-gaap_RightOfUseAssetObtainedInExchangeForOperatingLeaseLiability" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_RightOfUseAssetObtainedInExchangeForOperatingLeaseLiability"/>
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    <link:label id="lab_codi_ScheduleOfIntangibleAssetsByMajorClassTableTextBlock_cdab4fc4-00be-4e16-91e4-add73d4720c4_terseLabel_en-US" xlink:label="lab_codi_ScheduleOfIntangibleAssetsByMajorClassTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Summary of Other Intangible Assets</link:label>
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    <link:label id="lab_us-gaap_DeferredFinanceCostsNet_b04c9a0b-8e45-4acc-aa05-304ae9748c65_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, less accumulated amortization</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_BusinessAcquisitionAcquireeDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_BusinessAcquisitionAcquireeDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_BusinessAcquisitionAcquireeDomain" xlink:to="lab_us-gaap_BusinessAcquisitionAcquireeDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DisposalGroupNotDiscontinuedOperationGainLossOnDisposal_7288276e-2c89-4bcd-bf45-f28138825353_terseLabel_en-US" xlink:label="lab_us-gaap_DisposalGroupNotDiscontinuedOperationGainLossOnDisposal" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Disposal Group, Not Discontinued Operation, Gain (Loss) on Disposal</link:label>
    <link:label id="lab_us-gaap_DisposalGroupNotDiscontinuedOperationGainLossOnDisposal_label_en-US" xlink:label="lab_us-gaap_DisposalGroupNotDiscontinuedOperationGainLossOnDisposal" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Disposal Group, Not Discontinued Operation, Gain (Loss) on Disposal</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DisposalGroupNotDiscontinuedOperationGainLossOnDisposal" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DisposalGroupNotDiscontinuedOperationGainLossOnDisposal"/>
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    <link:label id="lab_codi_AnnualInternalRateOfReturn_f779761f-b773-4b65-b383-9bfe17668530_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>
    <link:label id="lab_codi_AnnualInternalRateOfReturn_label_en-US" xlink:label="lab_codi_AnnualInternalRateOfReturn" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Annual Internal Rate of Return</link:label>
    <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-20250331.xsd#codi_AnnualInternalRateOfReturn"/>
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    <link:label id="lab_us-gaap_FinanceLeaseLiabilityUndiscountedExcessAmount_b661f5ca-9766-4dbf-bcca-ad7be5a85b93_terseLabel_en-US" xlink:label="lab_us-gaap_FinanceLeaseLiabilityUndiscountedExcessAmount" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Finance Lease, Liability, Undiscounted Excess Amount</link:label>
    <link:label id="lab_us-gaap_FinanceLeaseLiabilityUndiscountedExcessAmount_label_en-US" xlink:label="lab_us-gaap_FinanceLeaseLiabilityUndiscountedExcessAmount" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Finance Lease, Liability, Undiscounted Excess Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FinanceLeaseLiabilityUndiscountedExcessAmount" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FinanceLeaseLiabilityUndiscountedExcessAmount"/>
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    <link:label id="lab_us-gaap_CommonStockSharesOutstanding_39cd454d-7cfb-4717-8c72-d88f0d19a86c_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 (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/2025/elts/us-gaap-2025.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_us-gaap_DiscontinuedOperationsPolicyTextBlock_8eadfd56-444f-4037-a7d5-49429ed14c8c_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, Policy [Policy Text Block]</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/2025/elts/us-gaap-2025.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_ProvisionForDoubtfulAccounts_382f8745-de85-4628-a3fe-522a3186c49b_terseLabel_en-US" xlink:label="lab_us-gaap_ProvisionForDoubtfulAccounts" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Accounts Receivable, Credit Loss Expense (Reversal)</link:label>
    <link:label id="lab_us-gaap_ProvisionForDoubtfulAccounts_label_en-US" xlink:label="lab_us-gaap_ProvisionForDoubtfulAccounts" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Accounts Receivable, Credit Loss Expense (Reversal)</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ProvisionForDoubtfulAccounts" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ProvisionForDoubtfulAccounts"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ProvisionForDoubtfulAccounts" xlink:to="lab_us-gaap_ProvisionForDoubtfulAccounts" xlink:type="arc" order="1"/>
    <link:label id="lab_srt_MedianMember_4b68b202-fc16-42fd-90d2-073480785247_terseLabel_en-US" xlink:label="lab_srt_MedianMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Median</link:label>
    <link:label id="lab_srt_MedianMember_label_en-US" xlink:label="lab_srt_MedianMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Median [Member]</link:label>
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    <link:label id="lab_dei_DocumentInformationTable_2784f450-6616-41db-9d7e-14b7a83977e7_terseLabel_en-US" xlink:label="lab_dei_DocumentInformationTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Document Information [Table]</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_dei_DocumentInformationTable" xlink:href="https://xbrl.sec.gov/dei/2025/dei-2025.xsd#dei_DocumentInformationTable"/>
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    <link:label id="lab_us-gaap_DisaggregationOfRevenueTableTextBlock_25132705-da27-4b79-9458-0dfa9d268876_terseLabel_en-US" xlink:label="lab_us-gaap_DisaggregationOfRevenueTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Disaggregation of Revenue</link:label>
    <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>
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    <link:label id="lab_us-gaap_IncomeLossFromContinuingOperationsBeforeIncomeTaxesMinorityInterestAndIncomeLossFromEquityMethodInvestments_dabbac0a-abf8-48b4-a7ba-804f35f9bd7d_terseLabel_en-US" xlink:label="lab_us-gaap_IncomeLossFromContinuingOperationsBeforeIncomeTaxesMinorityInterestAndIncomeLossFromEquityMethodInvestments" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Total consolidated income (loss) from continuing operations before income taxes</link:label>
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    <link:label id="lab_us-gaap_CorporateAndOtherMember_bc30c7bd-6ab4-42e5-8c7e-04655bc6854d_terseLabel_en-US" xlink:label="lab_us-gaap_CorporateAndOtherMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Corporate Segment and Other Operating Segment [Member]</link:label>
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    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CorporateAndOtherMember" xlink:to="lab_us-gaap_CorporateAndOtherMember" xlink:type="arc" order="1"/>
    <link:label id="lab_country_US_31ef0b07-94d4-4f61-aff1-5f37c00ef84c_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_IncreaseDecreaseInOperatingCapitalAbstract_bf7221d0-b7cc-4a78-9582-66f6ba480f72_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_codi_LeaseRightOfUseAsset_7818a8bb-ef78-41da-a2cd-475cb9d7dbbf_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>
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    <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_StockIssuedDuringPeriodValueStockOptionsExercised_069edf3f-f183-4aaf-bbff-3cd1edfd13cd_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>
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    <link:label id="lab_us-gaap_ScheduleOfProductWarrantyLiabilityTableTextBlock_3719524e-3763-458a-bd5e-eef7cc2eb738_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfProductWarrantyLiabilityTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Change in Carrying Value of Company's Warranty Liability</link:label>
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    <link:label id="lab_us-gaap_IncomeTaxExpenseBenefit_5d2288b9-2e22-49ea-acc5-e2920e8a40a2_terseLabel_en-US" xlink:label="lab_us-gaap_IncomeTaxExpenseBenefit" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Provision for income taxes</link:label>
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    <link:label id="lab_us-gaap_FairValueMeasurementsNonrecurringMember_f717f1de-7b1d-4aad-b2ea-51d5aa32830f_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, Nonrecurring [Member]</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DefinedContributionPlanEmployerDiscretionaryContributionAmount" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DefinedContributionPlanEmployerDiscretionaryContributionAmount"/>
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    <link:label id="lab_dei_CityAreaCode_6e3d4e7c-1138-4f97-b301-725c88b46320_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>
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    <link:label id="lab_us-gaap_ProceedsFromLongTermLinesOfCredit_fcf6f0d1-e6a8-4a44-b34c-c4e5d242e190_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 - revolving credit facility</link:label>
    <link:label id="lab_us-gaap_ProceedsFromLongTermLinesOfCredit_label_en-US" xlink:label="lab_us-gaap_ProceedsFromLongTermLinesOfCredit" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Proceeds from Long-Term Lines of Credit</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ProceedsFromLongTermLinesOfCredit" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ProceedsFromLongTermLinesOfCredit"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ProceedsFromLongTermLinesOfCredit" xlink:to="lab_us-gaap_ProceedsFromLongTermLinesOfCredit" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_NetCashProvidedByUsedInInvestingActivitiesAbstract_9c41ce09-7e7a-4426-ae78-5d4a78decf34_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">Cash flows from investing activities:</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">Cash Provided by (Used in) Investing Activity, Including Discontinued Operation [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_NetCashProvidedByUsedInInvestingActivitiesAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.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_NetCashProvidedByUsedInOperatingActivities_0a095c46-1e06-400e-984f-271ef76c5719_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, Total</link:label>
    <link:label id="lab_us-gaap_NetCashProvidedByUsedInOperatingActivities_label_en-US" xlink:label="lab_us-gaap_NetCashProvidedByUsedInOperatingActivities" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Cash Provided by (Used in) Operating Activity, Including Discontinued Operation</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_NetCashProvidedByUsedInOperatingActivities" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.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_codi_RepaymentsFromSubsidiaryBorrowings_019b0dcf-09f1-72d6-bea3-7491bf5227e2_negatedTerseLabel_en-US" xlink:label="lab_codi_RepaymentsFromSubsidiaryBorrowings" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Repayments From Subsidiary Borrowings</link:label>
    <link:label id="lab_codi_RepaymentsFromSubsidiaryBorrowings_label_en-US" xlink:label="lab_codi_RepaymentsFromSubsidiaryBorrowings" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Repayments From Subsidiary Borrowings</link:label>
    <link:label id="lab_codi_RepaymentsFromSubsidiaryBorrowings_documentation_en-US" xlink:label="lab_codi_RepaymentsFromSubsidiaryBorrowings" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Repayments From Subsidiary Borrowings</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_codi_RepaymentsFromSubsidiaryBorrowings" xlink:href="codi-20250331.xsd#codi_RepaymentsFromSubsidiaryBorrowings"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_codi_RepaymentsFromSubsidiaryBorrowings" xlink:to="lab_codi_RepaymentsFromSubsidiaryBorrowings" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_RelatedPartyTransactionsAbstract_71d52b6d-e466-4771-88c4-65028408e0a7_terseLabel_en-US" xlink:label="lab_us-gaap_RelatedPartyTransactionsAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Related Party Transactions [Abstract]</link:label>
    <link:label id="lab_us-gaap_RelatedPartyTransactionsAbstract_label_en-US" xlink:label="lab_us-gaap_RelatedPartyTransactionsAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Related Party Transactions [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_RelatedPartyTransactionsAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_RelatedPartyTransactionsAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_RelatedPartyTransactionsAbstract" xlink:to="lab_us-gaap_RelatedPartyTransactionsAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DefinedBenefitPlanAmortizationOfGainsLosses_79022c69-3cab-4cf8-9a78-6489531aab0d_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_DefinedBenefitPlanAmortizationOfGainsLosses" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Amortization of unrecognized loss</link:label>
    <link:label id="lab_us-gaap_DefinedBenefitPlanAmortizationOfGainsLosses_label_en-US" xlink:label="lab_us-gaap_DefinedBenefitPlanAmortizationOfGainsLosses" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Defined Benefit Plan, Amortization of Gain (Loss)</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DefinedBenefitPlanAmortizationOfGainsLosses" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DefinedBenefitPlanAmortizationOfGainsLosses"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DefinedBenefitPlanAmortizationOfGainsLosses" xlink:to="lab_us-gaap_DefinedBenefitPlanAmortizationOfGainsLosses" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_SubsequentEventMember_61ee18cf-19b7-4719-95e8-bf59b79b9a70_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</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/2025/elts/us-gaap-2025.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_codi_RelatedPartyVendorMember_0cbefd13-c055-4d2a-a986-79ffd1d1ef76_terseLabel_en-US" xlink:label="lab_codi_RelatedPartyVendorMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Related Party Vendor [Member]</link:label>
    <link:label id="lab_codi_RelatedPartyVendorMember_label_en-US" xlink:label="lab_codi_RelatedPartyVendorMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Related Party Vendor [Member]</link:label>
    <link:label id="lab_codi_RelatedPartyVendorMember_documentation_en-US" xlink:label="lab_codi_RelatedPartyVendorMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Related Party Vendor [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_codi_RelatedPartyVendorMember" xlink:href="codi-20250331.xsd#codi_RelatedPartyVendorMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_codi_RelatedPartyVendorMember" xlink:to="lab_codi_RelatedPartyVendorMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_SellingGeneralAndAdministrativeExpensesMember_ccba60bc-f6c8-4111-ac87-a06d9850c332_terseLabel_en-US" xlink:label="lab_us-gaap_SellingGeneralAndAdministrativeExpensesMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Selling, General and Administrative Expenses</link:label>
    <link:label id="lab_us-gaap_SellingGeneralAndAdministrativeExpensesMember_label_en-US" xlink:label="lab_us-gaap_SellingGeneralAndAdministrativeExpensesMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Selling, General and Administrative Expenses [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SellingGeneralAndAdministrativeExpensesMember" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_SellingGeneralAndAdministrativeExpensesMember"/>
    <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"/>
    <link:label id="lab_us-gaap_CostOfSalesMember_7a877c6e-6d79-49cb-90b6-99dbba43c93f_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/2025/elts/us-gaap-2025.xsd#us-gaap_CostOfSalesMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CostOfSalesMember" xlink:to="lab_us-gaap_CostOfSalesMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ScheduleOfEquityMethodInvestmentsLineItems_03555324-b130-41d6-b9cb-2c7a966edb82_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfEquityMethodInvestmentsLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Equity Method Investments [Line Items]</link:label>
    <link:label id="lab_us-gaap_ScheduleOfEquityMethodInvestmentsLineItems_label_en-US" xlink:label="lab_us-gaap_ScheduleOfEquityMethodInvestmentsLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Schedule of Equity Method Investments [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfEquityMethodInvestmentsLineItems" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ScheduleOfEquityMethodInvestmentsLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ScheduleOfEquityMethodInvestmentsLineItems" xlink:to="lab_us-gaap_ScheduleOfEquityMethodInvestmentsLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_codi_ProceedsFromMinorityShareholdersAcquisitions_ca464e73-60a3-4932-b9fd-3276cb4885f6_terseLabel_en-US" xlink:label="lab_codi_ProceedsFromMinorityShareholdersAcquisitions" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Proceeds From Minority Shareholders - Acquisitions</link:label>
    <link:label id="lab_codi_ProceedsFromMinorityShareholdersAcquisitions_label_en-US" xlink:label="lab_codi_ProceedsFromMinorityShareholdersAcquisitions" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Proceeds From Minority Shareholders - Acquisitions</link:label>
    <link:label id="lab_codi_ProceedsFromMinorityShareholdersAcquisitions_documentation_en-US" xlink:label="lab_codi_ProceedsFromMinorityShareholdersAcquisitions" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Proceeds From Minority Shareholders - Acquisitions</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_codi_ProceedsFromMinorityShareholdersAcquisitions" xlink:href="codi-20250331.xsd#codi_ProceedsFromMinorityShareholdersAcquisitions"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_codi_ProceedsFromMinorityShareholdersAcquisitions" xlink:to="lab_codi_ProceedsFromMinorityShareholdersAcquisitions" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_Goodwill_06c17336-9e11-4452-86b4-4189d85f7e7c_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_a9400815-51a1-4b70-bc81-34f9a3386150_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">Balance as of January 1, 2017</link:label>
    <link:label id="lab_us-gaap_Goodwill_cfa7b7a8-0a6d-448e-82be-6f60cd110157_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">Balance as of March 31, 2017</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/2025/elts/us-gaap-2025.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_codi_TotalUndiscountedLeasePayments_99094bd9-9d88-4a30-ac9f-51c72a0e88f4_terseLabel_en-US" xlink:label="lab_codi_TotalUndiscountedLeasePayments" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Total undiscounted lease payments</link:label>
    <link:label id="lab_codi_TotalUndiscountedLeasePayments_label_en-US" xlink:label="lab_codi_TotalUndiscountedLeasePayments" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Total undiscounted lease payments</link:label>
    <link:label id="lab_codi_TotalUndiscountedLeasePayments_documentation_en-US" xlink:label="lab_codi_TotalUndiscountedLeasePayments" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Total undiscounted lease payments</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_codi_TotalUndiscountedLeasePayments" xlink:href="codi-20250331.xsd#codi_TotalUndiscountedLeasePayments"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_codi_TotalUndiscountedLeasePayments" xlink:to="lab_codi_TotalUndiscountedLeasePayments" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LongtermDebtTypeAxis_b5c3bb69-47f5-4dbd-b9a7-0416cbd59a7d_terseLabel_en-US" xlink:label="lab_us-gaap_LongtermDebtTypeAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Long-term Debt, Type [Axis]</link:label>
    <link:label id="lab_us-gaap_LongtermDebtTypeAxis_label_en-US" xlink:label="lab_us-gaap_LongtermDebtTypeAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Long-Term Debt, Type [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LongtermDebtTypeAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_LongtermDebtTypeAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LongtermDebtTypeAxis" xlink:to="lab_us-gaap_LongtermDebtTypeAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_Depreciation_5101cc44-d1a0-45ef-bcd7-200e50bc4ca6_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/2025/elts/us-gaap-2025.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_FinanceLeaseLiabilityPaymentsDueYearFour_4984898b-936b-4d8a-b75b-4268426fb33e_terseLabel_en-US" xlink:label="lab_us-gaap_FinanceLeaseLiabilityPaymentsDueYearFour" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Finance Lease, Liability, to be Paid, Year Four</link:label>
    <link:label id="lab_us-gaap_FinanceLeaseLiabilityPaymentsDueYearFour_label_en-US" xlink:label="lab_us-gaap_FinanceLeaseLiabilityPaymentsDueYearFour" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Finance Lease, Liability, to be Paid, Year Four</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FinanceLeaseLiabilityPaymentsDueYearFour" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FinanceLeaseLiabilityPaymentsDueYearFour"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FinanceLeaseLiabilityPaymentsDueYearFour" xlink:to="lab_us-gaap_FinanceLeaseLiabilityPaymentsDueYearFour" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseRemainderOfFiscalYear_72290c68-7a64-4c82-b6fb-66e5c84c7fee_terseLabel_en-US" xlink:label="lab_us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseRemainderOfFiscalYear" 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_FiniteLivedIntangibleAssetsAmortizationExpenseRemainderOfFiscalYear_label_en-US" xlink:label="lab_us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseRemainderOfFiscalYear" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Finite-Lived Intangible Asset, Expected Amortization, Remainder of Fiscal Year</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseRemainderOfFiscalYear" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseRemainderOfFiscalYear"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseRemainderOfFiscalYear" xlink:to="lab_us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseRemainderOfFiscalYear" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedAssetsAbstract_162d303a-46d8-4daa-b76f-49426cc87206_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 Asset Acquired, Asset [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedAssetsAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.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_StatementEquityComponentsAxis_f18d31ec-271a-4cda-a235-9304caeb586e_terseLabel_en-US" xlink:label="lab_us-gaap_StatementEquityComponentsAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Equity Components [Axis]</link:label>
    <link:label id="lab_us-gaap_StatementEquityComponentsAxis_label_en-US" xlink:label="lab_us-gaap_StatementEquityComponentsAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Equity Components [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_StatementEquityComponentsAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_StatementEquityComponentsAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_StatementEquityComponentsAxis" xlink:to="lab_us-gaap_StatementEquityComponentsAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_PropertyPlantAndEquipmentLineItems_4b334e3a-b722-4138-a354-f8a665df23a5_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>
    <link:label id="lab_us-gaap_PropertyPlantAndEquipmentLineItems_label_en-US" xlink:label="lab_us-gaap_PropertyPlantAndEquipmentLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Property, Plant and Equipment [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PropertyPlantAndEquipmentLineItems" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_PropertyPlantAndEquipmentLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PropertyPlantAndEquipmentLineItems" xlink:to="lab_us-gaap_PropertyPlantAndEquipmentLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_codi_OptionActivityAttributableToNoncontrollingInterestHolders_8f36984e-5195-49c8-8e48-5da243958768_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 Interest Holders</link:label>
    <link:label id="lab_codi_OptionActivityAttributableToNoncontrollingInterestHolders_label_en-US" xlink:label="lab_codi_OptionActivityAttributableToNoncontrollingInterestHolders" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Option Activity Attributable To Noncontrolling Interest Holders</link:label>
    <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>
    <link:loc xlink:type="locator" xlink:label="loc_codi_OptionActivityAttributableToNoncontrollingInterestHolders" xlink:href="codi-20250331.xsd#codi_OptionActivityAttributableToNoncontrollingInterestHolders"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_codi_OptionActivityAttributableToNoncontrollingInterestHolders" xlink:to="lab_codi_OptionActivityAttributableToNoncontrollingInterestHolders" xlink:type="arc" order="1"/>
    <link:label id="lab_codi_AccruedDistributionPreferredShareholders_22e32b81-de68-408f-991c-b318562d1ca3_terseLabel_en-US" xlink:label="lab_codi_AccruedDistributionPreferredShareholders" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Accrued Distribution Preferred Shareholders</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-20250331.xsd#codi_AccruedDistributionPreferredShareholders"/>
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    <link:label id="lab_codi_StockholdersEquityTable_d71b187c-36f1-483b-84ea-92b7e5654f27_terseLabel_en-US" xlink:label="lab_codi_StockholdersEquityTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Stockholders Equity [Table]</link:label>
    <link:label id="lab_codi_StockholdersEquityTable_label_en-US" xlink:label="lab_codi_StockholdersEquityTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Stockholders Equity [Table]</link:label>
    <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-20250331.xsd#codi_StockholdersEquityTable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_codi_StockholdersEquityTable" xlink:to="lab_codi_StockholdersEquityTable" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_NumberOfReportableSegments_488d4cd9-9cab-4b39-b90a-ea9a64a5b648_verboseLabel_en-US" xlink:label="lab_us-gaap_NumberOfReportableSegments" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Number of reportable operating segments</link:label>
    <link:label id="lab_us-gaap_NumberOfReportableSegments_label_en-US" xlink:label="lab_us-gaap_NumberOfReportableSegments" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Number of Reportable Segments</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_NumberOfReportableSegments" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_NumberOfReportableSegments"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_NumberOfReportableSegments" xlink:to="lab_us-gaap_NumberOfReportableSegments" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CompensationAndEmployeeBenefitPlansTextBlock_fa6db5e6-dadf-4e13-be37-e0e943cac55c_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">Defined Benefit Plan</link:label>
    <link:label id="lab_us-gaap_CompensationAndEmployeeBenefitPlansTextBlock_label_en-US" xlink:label="lab_us-gaap_CompensationAndEmployeeBenefitPlansTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Compensation and Employee Benefit Plans [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CompensationAndEmployeeBenefitPlansTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_CompensationAndEmployeeBenefitPlansTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CompensationAndEmployeeBenefitPlansTextBlock" xlink:to="lab_us-gaap_CompensationAndEmployeeBenefitPlansTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedInventory_e836b2b6-363a-47ce-9b4e-396dd82dc0a7_terseLabel_en-US" xlink:label="lab_us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedInventory" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Business Combination, Recognized Asset Acquired, Inventory, Current</link:label>
    <link:label id="lab_us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedInventory_label_en-US" xlink:label="lab_us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedInventory" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Business Combination, Recognized Asset Acquired, Inventory, Current</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedInventory" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedInventory"/>
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    <link:label id="lab_us-gaap_ScenarioAdjustmentMember_e98043bc-017b-4cd7-9279-c5ceaf760b22_terseLabel_en-US" xlink:label="lab_us-gaap_ScenarioAdjustmentMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Scenario, Adjustment</link:label>
    <link:label id="lab_us-gaap_ScenarioAdjustmentMember_label_en-US" xlink:label="lab_us-gaap_ScenarioAdjustmentMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Scenario, Adjustment [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScenarioAdjustmentMember" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ScenarioAdjustmentMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ScenarioAdjustmentMember" xlink:to="lab_us-gaap_ScenarioAdjustmentMember" xlink:type="arc" order="1"/>
    <link:label id="lab_codi_LuganoFinancingArrangementsMember_019b0d9d-6e8f-7a1a-b104-ce8ad62a24a9_terseLabel_en-US" xlink:label="lab_codi_LuganoFinancingArrangementsMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Lugano Financing Arrangements</link:label>
    <link:label id="lab_codi_LuganoFinancingArrangementsMember_label_en-US" xlink:label="lab_codi_LuganoFinancingArrangementsMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Lugano Financing Arrangements [Member]</link:label>
    <link:label id="lab_codi_LuganoFinancingArrangementsMember_documentation_en-US" xlink:label="lab_codi_LuganoFinancingArrangementsMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Lugano Financing Arrangements</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_codi_LuganoFinancingArrangementsMember" xlink:href="codi-20250331.xsd#codi_LuganoFinancingArrangementsMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_codi_LuganoFinancingArrangementsMember" xlink:to="lab_codi_LuganoFinancingArrangementsMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedCurrentAssetsReceivables_76bdb44b-d103-4e31-807a-85ee7a208f29_terseLabel_en-US" xlink:label="lab_us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedCurrentAssetsReceivables" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Business Combination, Recognized Asset Acquired, Receivable, Current</link:label>
    <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 Asset Acquired, Receivable, Current</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedCurrentAssetsReceivables" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedCurrentAssetsReceivables"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedCurrentAssetsReceivables" xlink:to="lab_us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedCurrentAssetsReceivables" xlink:type="arc" order="1"/>
    <link:label id="lab_codi_AtTheMarketEquityOfferingPreferredMember_35953e81-cf40-4261-ae28-7c0832e69247_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-20250331.xsd#codi_AtTheMarketEquityOfferingPreferredMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_codi_AtTheMarketEquityOfferingPreferredMember" xlink:to="lab_codi_AtTheMarketEquityOfferingPreferredMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_GoodwillImpairedAccumulatedImpairmentLoss_3d433f21-cc61-49c5-bcfc-8ad1824742c1_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, estimated impairment loss</link:label>
    <link:label id="lab_us-gaap_GoodwillImpairedAccumulatedImpairmentLoss_c5280cd9-4adf-41a7-9257-3d6368e704e9_negatedLabel_en-US" xlink:label="lab_us-gaap_GoodwillImpairedAccumulatedImpairmentLoss" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:type="resource" xml:lang="en-US">Accumulated impairment losses (1)</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/2025/elts/us-gaap-2025.xsd#us-gaap_GoodwillImpairedAccumulatedImpairmentLoss"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_GoodwillImpairedAccumulatedImpairmentLoss" xlink:to="lab_us-gaap_GoodwillImpairedAccumulatedImpairmentLoss" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_PaymentsOfDebtIssuanceCosts_5c76bf65-184b-4916-93b0-88d369f53751_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_PaymentsOfDebtIssuanceCosts" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Payments of Debt Issuance Costs</link:label>
    <link:label id="lab_us-gaap_PaymentsOfDebtIssuanceCosts_label_en-US" xlink:label="lab_us-gaap_PaymentsOfDebtIssuanceCosts" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Payments of Debt Issuance Costs</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PaymentsOfDebtIssuanceCosts" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_PaymentsOfDebtIssuanceCosts"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PaymentsOfDebtIssuanceCosts" xlink:to="lab_us-gaap_PaymentsOfDebtIssuanceCosts" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DebtCurrent_a52f3129-abf5-47d7-a16c-0f4c62b415d4_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/2025/elts/us-gaap-2025.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_dei_EntityAddressStateOrProvince_6f8e26d6-a081-4272-a111-f1a0b62b9949_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>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityAddressStateOrProvince" xlink:href="https://xbrl.sec.gov/dei/2025/dei-2025.xsd#dei_EntityAddressStateOrProvince"/>
    <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_us-gaap_FinanceLeasePrincipalPayments_1963cd3b-bb1e-4b74-af20-d66e2a4ebdb3_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/2025/elts/us-gaap-2025.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"/>
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    <link:label id="lab_us-gaap_DebtInstrumentUnusedBorrowingCapacityAmount_019b23a7-d045-7c7b-9bef-fa217384d659_terseLabel_en-US" xlink:label="lab_us-gaap_DebtInstrumentUnusedBorrowingCapacityAmount" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Debt Instrument, Unused Borrowing Capacity, Amount</link:label>
    <link:label id="lab_us-gaap_DebtInstrumentUnusedBorrowingCapacityAmount_label_en-US" xlink:label="lab_us-gaap_DebtInstrumentUnusedBorrowingCapacityAmount" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Instrument, Unused Borrowing Capacity, Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtInstrumentUnusedBorrowingCapacityAmount" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DebtInstrumentUnusedBorrowingCapacityAmount"/>
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    <link:label id="lab_us-gaap_RelatedPartyDomain_28a69fc9-22ce-48da-95df-c6dd04339821_terseLabel_en-US" xlink:label="lab_us-gaap_RelatedPartyDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Related Party [Domain]</link:label>
    <link:label id="lab_us-gaap_RelatedPartyDomain_label_en-US" xlink:label="lab_us-gaap_RelatedPartyDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Related and Nonrelated Parties [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_RelatedPartyDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_RelatedPartyDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_RelatedPartyDomain" xlink:to="lab_us-gaap_RelatedPartyDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LiabilitiesCurrent_7cb68dd1-99f8-4716-878c-6cea7cf54048_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/2025/elts/us-gaap-2025.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_codi_OwnershipPercentageOfTrustInterestHeldByParentEntity_b4aac72e-8923-400e-a697-024f74e2ce49_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>
    <link:label id="lab_codi_OwnershipPercentageOfTrustInterestHeldByParentEntity_documentation_en-US" xlink:label="lab_codi_OwnershipPercentageOfTrustInterestHeldByParentEntity" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Ownership percentage of trust interest held by parent entity.</link:label>
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    <link:label id="lab_us-gaap_DerivativeInstrumentRiskAxis_11b4a94d-2e1c-4cfd-9f5d-8d4dd6a37eb7_terseLabel_en-US" xlink:label="lab_us-gaap_DerivativeInstrumentRiskAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Derivative Instrument [Axis]</link:label>
    <link:label id="lab_us-gaap_DerivativeInstrumentRiskAxis_label_en-US" xlink:label="lab_us-gaap_DerivativeInstrumentRiskAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Derivative Instrument [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DerivativeInstrumentRiskAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DerivativeInstrumentRiskAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DerivativeInstrumentRiskAxis" xlink:to="lab_us-gaap_DerivativeInstrumentRiskAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_RestrictedCash_019b17cf-b5ac-7564-9b39-f59488926cac_terseLabel_en-US" xlink:label="lab_us-gaap_RestrictedCash" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Restricted Cash</link:label>
    <link:label id="lab_us-gaap_RestrictedCash_label_en-US" xlink:label="lab_us-gaap_RestrictedCash" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Restricted Cash</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_RestrictedCash" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_RestrictedCash"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_RestrictedCash" xlink:to="lab_us-gaap_RestrictedCash" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_IncomeTaxAuthorityDomain_f3c11292-6ed8-47f9-82d5-a89fbe2ddc5a_terseLabel_en-US" xlink:label="lab_us-gaap_IncomeTaxAuthorityDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Income Tax Authority [Domain]</link:label>
    <link:label id="lab_us-gaap_IncomeTaxAuthorityDomain_label_en-US" xlink:label="lab_us-gaap_IncomeTaxAuthorityDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Income Tax Jurisdiction [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncomeTaxAuthorityDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_IncomeTaxAuthorityDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_IncomeTaxAuthorityDomain" xlink:to="lab_us-gaap_IncomeTaxAuthorityDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_RightOfUseAssetObtainedInExchangeForFinanceLeaseLiability_a04c8a8b-1a5d-4172-8c02-55a720d63796_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/2025/elts/us-gaap-2025.xsd#us-gaap_RightOfUseAssetObtainedInExchangeForFinanceLeaseLiability"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_RightOfUseAssetObtainedInExchangeForFinanceLeaseLiability" xlink:to="lab_us-gaap_RightOfUseAssetObtainedInExchangeForFinanceLeaseLiability" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_BusinessCombinationProvisionalInformationInitialAccountingIncompleteAdjustmentPropertyPlantAndEquipment_46b0a5ae-7134-4b4f-9657-b9204f5f1a26_terseLabel_en-US" xlink:label="lab_us-gaap_BusinessCombinationProvisionalInformationInitialAccountingIncompleteAdjustmentPropertyPlantAndEquipment" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Business Combination, Provisional Information, Initial Accounting Incomplete, Adjustment, Property, Plant, and Equipment</link:label>
    <link:label id="lab_us-gaap_BusinessCombinationProvisionalInformationInitialAccountingIncompleteAdjustmentPropertyPlantAndEquipment_label_en-US" xlink:label="lab_us-gaap_BusinessCombinationProvisionalInformationInitialAccountingIncompleteAdjustmentPropertyPlantAndEquipment" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Business Combination, Provisional Information, Initial Accounting Incomplete, Adjustment, Property, Plant, and Equipment</link:label>
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    <link:label id="lab_dei_EntityDomain_238a7efa-a6e1-443f-b595-9f3e3c57aecf_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>
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    <link:label id="lab_us-gaap_NetCashProvidedByUsedInInvestingActivities_c55bd9b1-c7d4-421d-82b3-476b75a4e6fe_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, Total</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">Cash Provided by (Used in) Investing Activity, Including Discontinued Operation</link:label>
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    <link:label id="lab_us-gaap_ProceedsFromMinorityShareholders_f4e4382b-7dc1-4167-9af5-dbaec801164f_terseLabel_en-US" xlink:label="lab_us-gaap_ProceedsFromMinorityShareholders" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Net proceeds provided by noncontrolling shareholders</link:label>
    <link:label id="lab_us-gaap_ProceedsFromMinorityShareholders_label_en-US" xlink:label="lab_us-gaap_ProceedsFromMinorityShareholders" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Proceeds from Noncontrolling Interests</link:label>
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    <link:label id="lab_dei_DocumentFiscalYearFocus_0450a9fe-a1c9-41f9-937e-dd6c1cf3f2f9_terseLabel_en-US" xlink:label="lab_dei_DocumentFiscalYearFocus" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Document Fiscal Year Focus</link:label>
    <link:label id="lab_dei_DocumentFiscalYearFocus_label_en-US" xlink:label="lab_dei_DocumentFiscalYearFocus" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Document Fiscal Year Focus</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_DocumentFiscalYearFocus" xlink:href="https://xbrl.sec.gov/dei/2025/dei-2025.xsd#dei_DocumentFiscalYearFocus"/>
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    <link:label id="lab_us-gaap_OperatingLeaseRightOfUseAsset_019b23c4-22eb-711b-8af2-c77f32222e54_terseLabel_en-US" xlink:label="lab_us-gaap_OperatingLeaseRightOfUseAsset" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Operating Lease, Right-of-Use Asset</link:label>
    <link:label id="lab_us-gaap_OperatingLeaseRightOfUseAsset_label_en-US" xlink:label="lab_us-gaap_OperatingLeaseRightOfUseAsset" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Operating Lease, Right-of-Use Asset</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OperatingLeaseRightOfUseAsset" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_OperatingLeaseRightOfUseAsset"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OperatingLeaseRightOfUseAsset" xlink:to="lab_us-gaap_OperatingLeaseRightOfUseAsset" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_MinorityInterestOwnershipPercentageByNoncontrollingOwners_e45ee2f8-c8bf-4fc0-8579-19ac7c49abc0_terseLabel_en-US" xlink:label="lab_us-gaap_MinorityInterestOwnershipPercentageByNoncontrollingOwners" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Subsidiary, Ownership Percentage, Noncontrolling Owner</link:label>
    <link:label id="lab_us-gaap_MinorityInterestOwnershipPercentageByNoncontrollingOwners_label_en-US" xlink:label="lab_us-gaap_MinorityInterestOwnershipPercentageByNoncontrollingOwners" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Subsidiary, Ownership Percentage, Noncontrolling Owner</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_MinorityInterestOwnershipPercentageByNoncontrollingOwners" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_MinorityInterestOwnershipPercentageByNoncontrollingOwners"/>
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    <link:label id="lab_us-gaap_EffectiveIncomeTaxRateContinuingOperations_56865626-cf32-4804-aa23-b8731bc46a7b_totalLabel_en-US" xlink:label="lab_us-gaap_EffectiveIncomeTaxRateContinuingOperations" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Effective income tax rate</link:label>
    <link:label id="lab_us-gaap_EffectiveIncomeTaxRateContinuingOperations_label_en-US" xlink:label="lab_us-gaap_EffectiveIncomeTaxRateContinuingOperations" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Effective Income Tax Rate Reconciliation, Percent</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_EffectiveIncomeTaxRateContinuingOperations" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_EffectiveIncomeTaxRateContinuingOperations"/>
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    <link:label id="lab_dei_EntityInteractiveDataCurrent_2989f8c1-11e9-4283-8c6b-7a1303b1271d_terseLabel_en-US" xlink:label="lab_dei_EntityInteractiveDataCurrent" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Entity Interactive Data Current</link:label>
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    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_EntityInteractiveDataCurrent" xlink:to="lab_dei_EntityInteractiveDataCurrent" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OperatingLeaseCost_b5a6ff20-4d67-4d4a-9092-87d95a41e7f9_terseLabel_en-US" xlink:label="lab_us-gaap_OperatingLeaseCost" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Operating lease cost</link:label>
    <link:label id="lab_us-gaap_OperatingLeaseCost_label_en-US" xlink:label="lab_us-gaap_OperatingLeaseCost" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Operating Lease, Cost</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OperatingLeaseCost" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_OperatingLeaseCost"/>
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    <link:label id="lab_us-gaap_OtherCommitmentsLineItems_748ccb5e-db8f-4928-860e-c05eaea19f05_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/2025/elts/us-gaap-2025.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"/>
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    <link:label id="lab_codi_SubsidiaryFinancingArrangementsBorrowings_documentation_en-US" xlink:label="lab_codi_SubsidiaryFinancingArrangementsBorrowings" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Subsidiary financing arrangements - borrowings</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncreaseDecreaseInStockholdersEquityRollForward" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_IncreaseDecreaseInStockholdersEquityRollForward"/>
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    <link:label id="lab_us-gaap_FiniteLivedIntangibleAssetsLineItems_332ebe84-b1f6-4014-97f5-9fd0efa96053_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>
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    <link:label id="lab_codi_BusinessCombinationProvisionalInformationInitialAccountingIncompleteAdjustmentOtherCurrentAndNoncurrentAssets_1d819eb3-7217-4d6a-b5c5-d7ef52426291_terseLabel_en-US" xlink:label="lab_codi_BusinessCombinationProvisionalInformationInitialAccountingIncompleteAdjustmentOtherCurrentAndNoncurrentAssets" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Other current and noncurrent assets</link:label>
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    <link:label id="lab_srt_OwnershipDomain_810a706e-ca0e-4f89-b79b-f61359c05182_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>
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    <link:label id="lab_us-gaap_ScheduleOfNetBenefitCostsTableTextBlock_e2f512c4-deb8-4db5-8af4-c1ac9b52d36b_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfNetBenefitCostsTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Summary of Net Periodic Benefit Cost</link:label>
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    <link:label id="lab_us-gaap_FinanceLeaseLiabilityPaymentsDueYearTwo_d4f3bf1e-f93b-4c78-947a-4b510a5c7444_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>
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    <link:label id="lab_us-gaap_AmortizationOfIntangibleAssets_d47af7ad-98fb-43f2-a437-cc53bbb8e233_terseLabel_en-US" xlink:label="lab_us-gaap_AmortizationOfIntangibleAssets" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Amortization expense</link:label>
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    <link:label id="lab_codi_OfficeFurnitureComputersAndSoftwareMember_26f2e7ca-edca-4fcf-96d6-f19012f2e156_terseLabel_en-US" xlink:label="lab_codi_OfficeFurnitureComputersAndSoftwareMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Furniture, fixtures and other</link:label>
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    <link:label id="lab_us-gaap_SellingGeneralAndAdministrativeExpense_b7bb3296-6fc7-45bb-aca8-20d7e10f6637_terseLabel_en-US" xlink:label="lab_us-gaap_SellingGeneralAndAdministrativeExpense" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Selling, general and administrative expense</link:label>
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    <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/2025/elts/us-gaap-2025.xsd#us-gaap_StockRepurchasedDuringPeriodValue"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_StockRepurchasedDuringPeriodValue" xlink:to="lab_us-gaap_StockRepurchasedDuringPeriodValue" xlink:type="arc" order="1"/>
    <link:label id="lab_codi_LicensingAndNonCompeteAgreementsMember_31d74ac6-2440-4cdf-a38b-24a24b9f0897_terseLabel_en-US" xlink:label="lab_codi_LicensingAndNonCompeteAgreementsMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Non-compete agreements</link:label>
    <link:label id="lab_codi_LicensingAndNonCompeteAgreementsMember_label_en-US" xlink:label="lab_codi_LicensingAndNonCompeteAgreementsMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Licensing And Non Compete Agreements [Member]</link:label>
    <link:label id="lab_codi_LicensingAndNonCompeteAgreementsMember_documentation_en-US" xlink:label="lab_codi_LicensingAndNonCompeteAgreementsMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Licensing and non-compete agreements.</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_codi_LicensingAndNonCompeteAgreementsMember" xlink:href="codi-20250331.xsd#codi_LicensingAndNonCompeteAgreementsMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_codi_LicensingAndNonCompeteAgreementsMember" xlink:to="lab_codi_LicensingAndNonCompeteAgreementsMember" xlink:type="arc" order="1"/>
    <link:label id="lab_codi_BusinessCombinationRecognizedIdentifiableAssetsAcquiredandLiabilitiesAssumedOtherAssets_2c18df64-2c98-4425-89af-109c61087ffe_terseLabel_en-US" xlink:label="lab_codi_BusinessCombinationRecognizedIdentifiableAssetsAcquiredandLiabilitiesAssumedOtherAssets" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Business Combination, Recognized Identifiable Assets Acquired and Liabilities Assumed, Current Assets, Prepaid Expense and Other Assets</link:label>
    <link:label id="lab_codi_BusinessCombinationRecognizedIdentifiableAssetsAcquiredandLiabilitiesAssumedOtherAssets_label_en-US" xlink:label="lab_codi_BusinessCombinationRecognizedIdentifiableAssetsAcquiredandLiabilitiesAssumedOtherAssets" 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 Other Assets</link:label>
    <link:label id="lab_codi_BusinessCombinationRecognizedIdentifiableAssetsAcquiredandLiabilitiesAssumedOtherAssets_documentation_en-US" xlink:label="lab_codi_BusinessCombinationRecognizedIdentifiableAssetsAcquiredandLiabilitiesAssumedOtherAssets" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Business Combination Recognized Identifiable Assets Acquired and Liabilities Assumed Other Assets</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_codi_BusinessCombinationRecognizedIdentifiableAssetsAcquiredandLiabilitiesAssumedOtherAssets" xlink:href="codi-20250331.xsd#codi_BusinessCombinationRecognizedIdentifiableAssetsAcquiredandLiabilitiesAssumedOtherAssets"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_codi_BusinessCombinationRecognizedIdentifiableAssetsAcquiredandLiabilitiesAssumedOtherAssets" xlink:to="lab_codi_BusinessCombinationRecognizedIdentifiableAssetsAcquiredandLiabilitiesAssumedOtherAssets" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_EntityCentralIndexKey_1ab186f9-450c-46e9-84ad-619f2e5fa106_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>
    <link:label id="lab_dei_EntityCentralIndexKey_label_en-US" xlink:label="lab_dei_EntityCentralIndexKey" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Entity Central Index Key</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityCentralIndexKey" xlink:href="https://xbrl.sec.gov/dei/2025/dei-2025.xsd#dei_EntityCentralIndexKey"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_EntityCentralIndexKey" xlink:to="lab_dei_EntityCentralIndexKey" xlink:type="arc" order="1"/>
    <link:label id="lab_codi_VelocityOutdoorMember_dbd2f127-5b62-42e4-91b3-60432214ccd8_terseLabel_en-US" xlink:label="lab_codi_VelocityOutdoorMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Total</link:label>
    <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>
    <link:loc xlink:type="locator" xlink:label="loc_codi_VelocityOutdoorMember" xlink:href="codi-20250331.xsd#codi_VelocityOutdoorMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_codi_VelocityOutdoorMember" xlink:to="lab_codi_VelocityOutdoorMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_InventoryFinishedGoods_78e3310e-b8f6-4a1f-ab5a-ecd53dc2f10a_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/2025/elts/us-gaap-2025.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_RevolvingCreditFacilityMember_8e7cb478-3d9f-401d-919b-57e4cce52ca9_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/2025/elts/us-gaap-2025.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_us-gaap_ScheduleOfEarningsPerShareBasicByCommonClassTextBlock_978f3ff6-c285-4086-8d0e-bb44e631e88b_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfEarningsPerShareBasicByCommonClassTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Summary of Basic and Diluted Earnings Per Share</link:label>
    <link:label id="lab_us-gaap_ScheduleOfEarningsPerShareBasicByCommonClassTextBlock_label_en-US" xlink:label="lab_us-gaap_ScheduleOfEarningsPerShareBasicByCommonClassTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Schedule of Earnings Per Share, Basic, by Common Class, Including Two Class Method [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfEarningsPerShareBasicByCommonClassTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ScheduleOfEarningsPerShareBasicByCommonClassTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ScheduleOfEarningsPerShareBasicByCommonClassTextBlock" xlink:to="lab_us-gaap_ScheduleOfEarningsPerShareBasicByCommonClassTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FinanceLeaseLiability_28d136b2-c560-400a-bb38-976644d9b3b4_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/2025/elts/us-gaap-2025.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"/>
    <link:label id="lab_us-gaap_ScheduleOfSegmentReportingInformationBySegmentTable_e82542f8-e3fe-455f-818b-06d096837c9c_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfSegmentReportingInformationBySegmentTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Segment Reporting Information, by Segment [Table]</link:label>
    <link:label id="lab_us-gaap_ScheduleOfSegmentReportingInformationBySegmentTable_label_en-US" xlink:label="lab_us-gaap_ScheduleOfSegmentReportingInformationBySegmentTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Schedule of Segment Reporting Information, by Segment [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfSegmentReportingInformationBySegmentTable" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ScheduleOfSegmentReportingInformationBySegmentTable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ScheduleOfSegmentReportingInformationBySegmentTable" xlink:to="lab_us-gaap_ScheduleOfSegmentReportingInformationBySegmentTable" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_GoodwillFairValueDisclosure_4e143986-08a2-46fc-87be-993827c2f0eb_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>
    <link:label id="lab_us-gaap_GoodwillFairValueDisclosure_label_en-US" xlink:label="lab_us-gaap_GoodwillFairValueDisclosure" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Goodwill, Fair Value Disclosure</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_GoodwillFairValueDisclosure" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_GoodwillFairValueDisclosure"/>
    <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"/>
    <link:label id="lab_us-gaap_InventoryRawMaterialsAndSupplies_6b0865db-ad68-4636-9940-d9affeb89fec_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</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>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_InventoryRawMaterialsAndSupplies" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_InventoryRawMaterialsAndSupplies"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_InventoryRawMaterialsAndSupplies" xlink:to="lab_us-gaap_InventoryRawMaterialsAndSupplies" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_IncreaseDecreaseInPrepaidDeferredExpenseAndOtherAssets_906e6f64-4ce6-48c1-bb45-b7a178a879c8_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/2025/elts/us-gaap-2025.xsd#us-gaap_IncreaseDecreaseInPrepaidDeferredExpenseAndOtherAssets"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_IncreaseDecreaseInPrepaidDeferredExpenseAndOtherAssets" xlink:to="lab_us-gaap_IncreaseDecreaseInPrepaidDeferredExpenseAndOtherAssets" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_StatementBusinessSegmentsAxis_b80d718d-5f05-419c-8e96-6f643d97a590_terseLabel_en-US" xlink:label="lab_us-gaap_StatementBusinessSegmentsAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Segments [Axis]</link:label>
    <link:label id="lab_us-gaap_StatementBusinessSegmentsAxis_label_en-US" xlink:label="lab_us-gaap_StatementBusinessSegmentsAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Segments [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_StatementBusinessSegmentsAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_StatementBusinessSegmentsAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_StatementBusinessSegmentsAxis" xlink:to="lab_us-gaap_StatementBusinessSegmentsAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_codi_Debtissuanceaggregateprincipalamount_a0076bd2-e082-41a5-b3aa-ab1c54047a45_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>
    <link:loc xlink:type="locator" xlink:label="loc_codi_Debtissuanceaggregateprincipalamount" xlink:href="codi-20250331.xsd#codi_Debtissuanceaggregateprincipalamount"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_codi_Debtissuanceaggregateprincipalamount" xlink:to="lab_codi_Debtissuanceaggregateprincipalamount" xlink:type="arc" order="1"/>
    <link:label id="lab_codi_LeaseSupplementalBalanceSheetInformationTableTableTextBlock_52a66eaf-8417-40c6-8d8b-a1a518c6b2e2_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-20250331.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_dei_EntityFilerCategory_de8a7d9a-1480-49ac-8fc1-ea01d9811451_terseLabel_en-US" xlink:label="lab_dei_EntityFilerCategory" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Entity Filer Category</link:label>
    <link:label id="lab_dei_EntityFilerCategory_label_en-US" xlink:label="lab_dei_EntityFilerCategory" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Entity Filer Category</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityFilerCategory" xlink:href="https://xbrl.sec.gov/dei/2025/dei-2025.xsd#dei_EntityFilerCategory"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_EntityFilerCategory" xlink:to="lab_dei_EntityFilerCategory" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_IncomeAmountsAttributableToReportingEntityDisclosuresAbstract_3d95ebcd-2fa9-45d6-b20c-9b73730894d0_terseLabel_en-US" xlink:label="lab_us-gaap_IncomeAmountsAttributableToReportingEntityDisclosuresAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Amounts attributable to Holdings</link:label>
    <link:label id="lab_us-gaap_IncomeAmountsAttributableToReportingEntityDisclosuresAbstract_label_en-US" xlink:label="lab_us-gaap_IncomeAmountsAttributableToReportingEntityDisclosuresAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Income Amounts Attributable to Parent, Disclosures [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncomeAmountsAttributableToReportingEntityDisclosuresAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_IncomeAmountsAttributableToReportingEntityDisclosuresAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_IncomeAmountsAttributableToReportingEntityDisclosuresAbstract" xlink:to="lab_us-gaap_IncomeAmountsAttributableToReportingEntityDisclosuresAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_LocalPhoneNumber_aeb7c5e8-eb36-49b1-955d-4fbd528e609e_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>
    <link:label id="lab_dei_LocalPhoneNumber_label_en-US" xlink:label="lab_dei_LocalPhoneNumber" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Local Phone Number</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_LocalPhoneNumber" xlink:href="https://xbrl.sec.gov/dei/2025/dei-2025.xsd#dei_LocalPhoneNumber"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_LocalPhoneNumber" xlink:to="lab_dei_LocalPhoneNumber" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ClassOfStockDomain_33775db5-eb17-4858-b272-45d7806902e4_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>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ClassOfStockDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ClassOfStockDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ClassOfStockDomain" xlink:to="lab_us-gaap_ClassOfStockDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_codi_GoodwillImpairmentTestingFairValueExceedingCarryingValuePercent_3ecdcdc2-747b-4330-a2e5-6a9dc3b631d9_terseLabel_en-US" xlink:label="lab_codi_GoodwillImpairmentTestingFairValueExceedingCarryingValuePercent" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Goodwill Impairment Testing, Fair Value Exceeding Carrying Value, Percent</link:label>
    <link:label id="lab_codi_GoodwillImpairmentTestingFairValueExceedingCarryingValuePercent_label_en-US" xlink:label="lab_codi_GoodwillImpairmentTestingFairValueExceedingCarryingValuePercent" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Goodwill Impairment Testing, Fair Value Exceeding Carrying Value, Percent</link:label>
    <link:label id="lab_codi_GoodwillImpairmentTestingFairValueExceedingCarryingValuePercent_documentation_en-US" xlink:label="lab_codi_GoodwillImpairmentTestingFairValueExceedingCarryingValuePercent" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Goodwill Impairment Testing, Fair Value Exceeding Carrying Value, Percent</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_codi_GoodwillImpairmentTestingFairValueExceedingCarryingValuePercent" xlink:href="codi-20250331.xsd#codi_GoodwillImpairmentTestingFairValueExceedingCarryingValuePercent"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_codi_GoodwillImpairmentTestingFairValueExceedingCarryingValuePercent" xlink:to="lab_codi_GoodwillImpairmentTestingFairValueExceedingCarryingValuePercent" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CommonStockNoParValue_6b89c7ff-b291-42ee-8d63-7143d84e63f7_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/2025/elts/us-gaap-2025.xsd#us-gaap_CommonStockNoParValue"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CommonStockNoParValue" xlink:to="lab_us-gaap_CommonStockNoParValue" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_EffectiveIncomeTaxRateReconciliationAtFederalStatutoryIncomeTaxRate_de32df0e-f2c9-481f-a66a-3a5544227a9b_terseLabel_en-US" xlink:label="lab_us-gaap_EffectiveIncomeTaxRateReconciliationAtFederalStatutoryIncomeTaxRate" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">United States Federal Statutory Rate</link:label>
    <link:label id="lab_us-gaap_EffectiveIncomeTaxRateReconciliationAtFederalStatutoryIncomeTaxRate_label_en-US" xlink:label="lab_us-gaap_EffectiveIncomeTaxRateReconciliationAtFederalStatutoryIncomeTaxRate" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Effective Income Tax Rate Reconciliation, at Federal Statutory Income Tax Rate, Percent</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_EffectiveIncomeTaxRateReconciliationAtFederalStatutoryIncomeTaxRate" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_EffectiveIncomeTaxRateReconciliationAtFederalStatutoryIncomeTaxRate"/>
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    <link:label id="lab_srt_EuropeMember_d8df12f7-0574-4067-8316-6fe87fd617b6_terseLabel_en-US" xlink:label="lab_srt_EuropeMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Europe [Member]</link:label>
    <link:label id="lab_srt_EuropeMember_label_en-US" xlink:label="lab_srt_EuropeMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Europe [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_srt_EuropeMember" xlink:href="https://xbrl.fasb.org/srt/2025/elts/srt-2025.xsd#srt_EuropeMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_srt_EuropeMember" xlink:to="lab_srt_EuropeMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_PaymentsForProceedsFromOtherInvestingActivities_05f79aa2-8fba-4cc8-ba0d-75dacadb3abc_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">Payment for (Proceeds from) Other Investing Activity</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PaymentsForProceedsFromOtherInvestingActivities" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.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_LongTermDebtMaturitiesRepaymentsOfPrincipalAfterYearFive_96254d16-3df3-4a59-be9f-476496b4da0d_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/2025/elts/us-gaap-2025.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_SubsequentEventTypeAxis_6097287c-658e-4514-9c97-67761c713d38_terseLabel_en-US" xlink:label="lab_us-gaap_SubsequentEventTypeAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Subsequent Event Type [Axis]</link:label>
    <link:label id="lab_us-gaap_SubsequentEventTypeAxis_label_en-US" xlink:label="lab_us-gaap_SubsequentEventTypeAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Subsequent Event Type [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SubsequentEventTypeAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_SubsequentEventTypeAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_SubsequentEventTypeAxis" xlink:to="lab_us-gaap_SubsequentEventTypeAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedIntangibleAssetsOtherThanGoodwill_f1c9459e-c92c-4a44-85bc-005a94bddd34_terseLabel_en-US" xlink:label="lab_us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedIntangibleAssetsOtherThanGoodwill" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Business Combination, Recognized Asset Acquired, Identifiable Intangible Asset, Excluding Goodwill</link:label>
    <link:label id="lab_us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedIntangibleAssetsOtherThanGoodwill_label_en-US" xlink:label="lab_us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedIntangibleAssetsOtherThanGoodwill" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Business Combination, Recognized Asset Acquired, Identifiable Intangible Asset, Excluding Goodwill</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedIntangibleAssetsOtherThanGoodwill" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedIntangibleAssetsOtherThanGoodwill"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedIntangibleAssetsOtherThanGoodwill" xlink:to="lab_us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedIntangibleAssetsOtherThanGoodwill" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedCashAndEquivalents_6121685f-1703-46e5-93ca-e829652501ca_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">Business Combination, Recognized Asset Acquired, Cash and Cash Equivalent</link:label>
    <link:label id="lab_us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedCashAndEquivalents_label_en-US" xlink:label="lab_us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedCashAndEquivalents" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Business Combination, Recognized Asset Acquired, Cash and Cash Equivalent</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedCashAndEquivalents" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedCashAndEquivalents"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedCashAndEquivalents" xlink:to="lab_us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedCashAndEquivalents" xlink:type="arc" order="1"/>
    <link:label id="lab_codi_DisposalGroupTotalenterprisevalue_db73ae14-6452-4846-a414-455b7a8b31a0_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>
    <link:loc xlink:type="locator" xlink:label="loc_codi_DisposalGroupTotalenterprisevalue" xlink:href="codi-20250331.xsd#codi_DisposalGroupTotalenterprisevalue"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_codi_DisposalGroupTotalenterprisevalue" xlink:to="lab_codi_DisposalGroupTotalenterprisevalue" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AssetsAbstract_d6d16f59-de0b-4f3c-a84c-ebe9a8ee38f4_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>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AssetsAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_AssetsAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AssetsAbstract" xlink:to="lab_us-gaap_AssetsAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LongTermDebtNoncurrent_c53a3952-785b-4659-8f4f-7fc3a1dc222b_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 (refer to Note H)</link:label>
    <link:label id="lab_us-gaap_LongTermDebtNoncurrent_92d3952d-5a5e-4f92-909b-59db4e881d86_terseLabel_en-US" xlink:label="lab_us-gaap_LongTermDebtNoncurrent" 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_LongTermDebtNoncurrent_label_en-US" xlink:label="lab_us-gaap_LongTermDebtNoncurrent" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Long-Term Debt, Excluding Current Maturities</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LongTermDebtNoncurrent" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_LongTermDebtNoncurrent"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LongTermDebtNoncurrent" xlink:to="lab_us-gaap_LongTermDebtNoncurrent" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CreditFacilityAxis_0cc7c397-b9a0-4854-a059-1ce84a512474_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/2025/elts/us-gaap-2025.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_BalanceSheetLocationAxis_2cf07b4b-2454-4631-907b-37cc2e2b3d21_terseLabel_en-US" xlink:label="lab_us-gaap_BalanceSheetLocationAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Balance Sheet Location [Axis]</link:label>
    <link:label id="lab_us-gaap_BalanceSheetLocationAxis_label_en-US" xlink:label="lab_us-gaap_BalanceSheetLocationAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Statement of Financial Position Location, Balance [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_BalanceSheetLocationAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_BalanceSheetLocationAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_BalanceSheetLocationAxis" xlink:to="lab_us-gaap_BalanceSheetLocationAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseYearThree_19cdea95-469c-458d-aa38-8f4de5ecf9a1_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">2024</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/2025/elts/us-gaap-2025.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_PrimaloftMember_eaabbc1a-9f07-4822-8aee-46723f83e772_terseLabel_en-US" xlink:label="lab_codi_PrimaloftMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Primaloft</link:label>
    <link:label id="lab_codi_PrimaloftMember_label_en-US" xlink:label="lab_codi_PrimaloftMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Primaloft [Member]</link:label>
    <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-20250331.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_LoansAndLeasesReceivableRelatedParties_019b0dc2-82be-74eb-aada-7e04287d9868_terseLabel_en-US" xlink:label="lab_us-gaap_LoansAndLeasesReceivableRelatedParties" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Loans and Leases Receivable, Related Parties</link:label>
    <link:label id="lab_us-gaap_LoansAndLeasesReceivableRelatedParties_label_en-US" xlink:label="lab_us-gaap_LoansAndLeasesReceivableRelatedParties" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Loans and Leases Receivable, Related Parties</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LoansAndLeasesReceivableRelatedParties" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_LoansAndLeasesReceivableRelatedParties"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LoansAndLeasesReceivableRelatedParties" xlink:to="lab_us-gaap_LoansAndLeasesReceivableRelatedParties" xlink:type="arc" order="1"/>
    <link:label id="lab_codi_OwnershipPercentageRelatedPartyVendors_b6fa951d-8ebc-4fac-95d3-45f6992a2575_terseLabel_en-US" xlink:label="lab_codi_OwnershipPercentageRelatedPartyVendors" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Ownership Percentage, Related Party Vendors</link:label>
    <link:label id="lab_codi_OwnershipPercentageRelatedPartyVendors_label_en-US" xlink:label="lab_codi_OwnershipPercentageRelatedPartyVendors" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Ownership Percentage, Related Party Vendors</link:label>
    <link:label id="lab_codi_OwnershipPercentageRelatedPartyVendors_documentation_en-US" xlink:label="lab_codi_OwnershipPercentageRelatedPartyVendors" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Ownership Percentage, Related Party Vendors</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_codi_OwnershipPercentageRelatedPartyVendors" xlink:href="codi-20250331.xsd#codi_OwnershipPercentageRelatedPartyVendors"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_codi_OwnershipPercentageRelatedPartyVendors" xlink:to="lab_codi_OwnershipPercentageRelatedPartyVendors" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DebtInstrumentAxis_33c84fa2-6402-40fa-bf0b-3bac15db35c6_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/2025/elts/us-gaap-2025.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_us-gaap_FairValueDisclosuresTextBlock_1d2d225f-c748-4a7a-a58d-adedc74557f4_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/2025/elts/us-gaap-2025.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_us-gaap_BusinessAcquisitionLineItems_d549a00e-d7c6-4e0a-80da-7ffc0fa99e08_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 Combination [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 Combination [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_BusinessAcquisitionLineItems" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.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_CreditFacilityDomain_494129ff-4bc6-4c63-9963-5dd656789b22_terseLabel_en-US" xlink:label="lab_us-gaap_CreditFacilityDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Credit Facility [Domain]</link:label>
    <link:label id="lab_us-gaap_CreditFacilityDomain_label_en-US" xlink:label="lab_us-gaap_CreditFacilityDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Credit Facility [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CreditFacilityDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_CreditFacilityDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CreditFacilityDomain" xlink:to="lab_us-gaap_CreditFacilityDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FiniteLivedIntangibleAssetsGross_f4d04a37-9ad6-46e5-8b5c-b2ffff618094_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">Other 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/2025/elts/us-gaap-2025.xsd#us-gaap_FiniteLivedIntangibleAssetsGross"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FiniteLivedIntangibleAssetsGross" xlink:to="lab_us-gaap_FiniteLivedIntangibleAssetsGross" xlink:type="arc" order="1"/>
    <link:label id="lab_codi_ArnoldMember_ce296d2f-2a14-4e0c-9c46-9c560d6eebed_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 [Member]</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-20250331.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_dei_EntityAddressAddressLine1_6f135b39-8a89-4dec-a691-15dfacdd3558_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/2025/dei-2025.xsd#dei_EntityAddressAddressLine1"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_EntityAddressAddressLine1" xlink:to="lab_dei_EntityAddressAddressLine1" xlink:type="arc" order="1"/>
    <link:label id="lab_codi_ManagementServiceAgreementWithCGMMember_551943e2-1e50-4101-b1fb-af0045286527_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-20250331.xsd#codi_ManagementServiceAgreementWithCGMMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_codi_ManagementServiceAgreementWithCGMMember" xlink:to="lab_codi_ManagementServiceAgreementWithCGMMember" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_EntityAddressAddressLine2_4363174e-7c50-4a69-9fd4-75be502a6163_terseLabel_en-US" xlink:label="lab_dei_EntityAddressAddressLine2" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Entity Address, Address Line Two</link:label>
    <link:label id="lab_dei_EntityAddressAddressLine2_label_en-US" xlink:label="lab_dei_EntityAddressAddressLine2" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Entity Address, Address Line Two</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityAddressAddressLine2" xlink:href="https://xbrl.sec.gov/dei/2025/dei-2025.xsd#dei_EntityAddressAddressLine2"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_EntityAddressAddressLine2" xlink:to="lab_dei_EntityAddressAddressLine2" xlink:type="arc" order="1"/>
    <link:label id="lab_codi_PercentageOwnershipPrimaryMember_154ba767-ebb0-46e6-bd7f-bcf81c9e174b_terseLabel_en-US" xlink:label="lab_codi_PercentageOwnershipPrimaryMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">% Ownership Primary</link:label>
    <link:label id="lab_codi_PercentageOwnershipPrimaryMember_label_en-US" xlink:label="lab_codi_PercentageOwnershipPrimaryMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Percentage Ownership Primary [Member]</link:label>
    <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-20250331.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_AccumulatedOtherComprehensiveIncomeMember_7cf442e3-70a3-49f8-a795-fea8d0530c36_terseLabel_en-US" xlink:label="lab_us-gaap_AccumulatedOtherComprehensiveIncomeMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">AOCI Attributable to Parent [Member]</link:label>
    <link:label id="lab_us-gaap_AccumulatedOtherComprehensiveIncomeMember_label_en-US" xlink:label="lab_us-gaap_AccumulatedOtherComprehensiveIncomeMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">AOCI Attributable to Parent [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AccumulatedOtherComprehensiveIncomeMember" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_AccumulatedOtherComprehensiveIncomeMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AccumulatedOtherComprehensiveIncomeMember" xlink:to="lab_us-gaap_AccumulatedOtherComprehensiveIncomeMember" xlink:type="arc" order="1"/>
    <link:label id="lab_srt_ScheduleOfEquityMethodInvestmentEquityMethodInvesteeNameAxis_8ab91851-2307-48b7-9f43-816d506aa679_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/2025/elts/srt-2025.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_DebtInstrumentInterestRateStatedPercentage_96b5afa4-221d-45d4-8c82-461bf5e3bea3_terseLabel_en-US" xlink:label="lab_us-gaap_DebtInstrumentInterestRateStatedPercentage" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Debt Instrument, Interest Rate, Stated Percentage</link:label>
    <link:label id="lab_us-gaap_DebtInstrumentInterestRateStatedPercentage_label_en-US" xlink:label="lab_us-gaap_DebtInstrumentInterestRateStatedPercentage" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Instrument, Interest Rate, Stated Percentage</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtInstrumentInterestRateStatedPercentage" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DebtInstrumentInterestRateStatedPercentage"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DebtInstrumentInterestRateStatedPercentage" xlink:to="lab_us-gaap_DebtInstrumentInterestRateStatedPercentage" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OperatingLeaseLiabilityNoncurrent_019b23d2-9d32-729f-89b7-3ba1dd7e8c5c_terseLabel_en-US" xlink:label="lab_us-gaap_OperatingLeaseLiabilityNoncurrent" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Operating Lease, Liability, Noncurrent</link:label>
    <link:label id="lab_us-gaap_OperatingLeaseLiabilityNoncurrent_label_en-US" xlink:label="lab_us-gaap_OperatingLeaseLiabilityNoncurrent" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Operating Lease, Liability, Noncurrent</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OperatingLeaseLiabilityNoncurrent" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_OperatingLeaseLiabilityNoncurrent"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OperatingLeaseLiabilityNoncurrent" xlink:to="lab_us-gaap_OperatingLeaseLiabilityNoncurrent" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DisposalGroupIncludingDiscontinuedOperationOperatingIncomeLoss_1129ddb3-4cd8-4b4e-b3c1-cf34b82f72d9_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">Disposal Group, Including Discontinued Operation, Operating Income (Loss)</link:label>
    <link:label id="lab_us-gaap_DisposalGroupIncludingDiscontinuedOperationOperatingIncomeLoss_564eb845-7cc6-4667-a19e-9b9736deb117_verboseLabel_en-US" xlink:label="lab_us-gaap_DisposalGroupIncludingDiscontinuedOperationOperatingIncomeLoss" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Operating income (loss)</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>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DisposalGroupIncludingDiscontinuedOperationOperatingIncomeLoss" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DisposalGroupIncludingDiscontinuedOperationOperatingIncomeLoss"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DisposalGroupIncludingDiscontinuedOperationOperatingIncomeLoss" xlink:to="lab_us-gaap_DisposalGroupIncludingDiscontinuedOperationOperatingIncomeLoss" xlink:type="arc" order="1"/>
    <link:label id="lab_codi_PaymentsOfDistributionsToShareholders_82316efc-6a72-41f2-80e1-add951413ab2_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>
    <link:label id="lab_codi_PaymentsOfDistributionsToShareholders_e3c14ef3-0a98-4590-87e9-91d50316f6f7_terseLabel_en-US" xlink:label="lab_codi_PaymentsOfDistributionsToShareholders" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Distributions paid</link:label>
    <link:label id="lab_codi_PaymentsOfDistributionsToShareholders_label_en-US" xlink:label="lab_codi_PaymentsOfDistributionsToShareholders" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Payments Of Distributions To Shareholders</link:label>
    <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>
    <link:loc xlink:type="locator" xlink:label="loc_codi_PaymentsOfDistributionsToShareholders" xlink:href="codi-20250331.xsd#codi_PaymentsOfDistributionsToShareholders"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_codi_PaymentsOfDistributionsToShareholders" xlink:to="lab_codi_PaymentsOfDistributionsToShareholders" xlink:type="arc" order="1"/>
    <link:label id="lab_codi_ArnoldMagneticsMember_e6b79646-76b4-439f-a4d8-c3958339d306_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 [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>
    <link:loc xlink:type="locator" xlink:label="loc_codi_ArnoldMagneticsMember" xlink:href="codi-20250331.xsd#codi_ArnoldMagneticsMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_codi_ArnoldMagneticsMember" xlink:to="lab_codi_ArnoldMagneticsMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_InventoryWorkInProcess_a6a7da14-f0c0-4da9-9f94-dc7d439323f4_terseLabel_en-US" xlink:label="lab_us-gaap_InventoryWorkInProcess" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Work-in-process</link:label>
    <link:label id="lab_us-gaap_InventoryWorkInProcess_label_en-US" xlink:label="lab_us-gaap_InventoryWorkInProcess" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Inventory, Work in Process, Gross</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_InventoryWorkInProcess" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_InventoryWorkInProcess"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_InventoryWorkInProcess" xlink:to="lab_us-gaap_InventoryWorkInProcess" xlink:type="arc" order="1"/>
    <link:label id="lab_srt_OwnershipAxis_5b932b59-86cb-480b-b1f7-8b492ae420be_terseLabel_en-US" xlink:label="lab_srt_OwnershipAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Ownership [Axis]</link:label>
    <link:label id="lab_srt_OwnershipAxis_label_en-US" xlink:label="lab_srt_OwnershipAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Ownership [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_srt_OwnershipAxis" xlink:href="https://xbrl.fasb.org/srt/2025/elts/srt-2025.xsd#srt_OwnershipAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_srt_OwnershipAxis" xlink:to="lab_srt_OwnershipAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DefinedBenefitPlanAmortizationOfPriorServiceCostCredit_5c037275-6e8e-44c0-a68c-227cdb20211c_terseLabel_en-US" xlink:label="lab_us-gaap_DefinedBenefitPlanAmortizationOfPriorServiceCostCredit" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Defined Benefit Plan, Amortization of Prior Service Cost (Credit)</link:label>
    <link:label id="lab_us-gaap_DefinedBenefitPlanAmortizationOfPriorServiceCostCredit_label_en-US" xlink:label="lab_us-gaap_DefinedBenefitPlanAmortizationOfPriorServiceCostCredit" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Defined Benefit Plan, Amortization of Prior Service Cost (Credit)</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DefinedBenefitPlanAmortizationOfPriorServiceCostCredit" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DefinedBenefitPlanAmortizationOfPriorServiceCostCredit"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DefinedBenefitPlanAmortizationOfPriorServiceCostCredit" xlink:to="lab_us-gaap_DefinedBenefitPlanAmortizationOfPriorServiceCostCredit" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_IncomeStatementBalanceSheetAndAdditionalDisclosuresByDisposalGroupsIncludingDiscontinuedOperationsLineItems_252600d9-2ab2-446d-a21d-f888d2a5fa4b_terseLabel_en-US" xlink:label="lab_us-gaap_IncomeStatementBalanceSheetAndAdditionalDisclosuresByDisposalGroupsIncludingDiscontinuedOperationsLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Income Statement, Balance Sheet and Additional Disclosures by Disposal Groups, Including Discontinued Operations [Line Items]</link:label>
    <link:label id="lab_us-gaap_IncomeStatementBalanceSheetAndAdditionalDisclosuresByDisposalGroupsIncludingDiscontinuedOperationsLineItems_label_en-US" xlink:label="lab_us-gaap_IncomeStatementBalanceSheetAndAdditionalDisclosuresByDisposalGroupsIncludingDiscontinuedOperationsLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Income Statement, Balance Sheet and Additional Disclosures by Disposal Groups, Including Discontinued Operations [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncomeStatementBalanceSheetAndAdditionalDisclosuresByDisposalGroupsIncludingDiscontinuedOperationsLineItems" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_IncomeStatementBalanceSheetAndAdditionalDisclosuresByDisposalGroupsIncludingDiscontinuedOperationsLineItems"/>
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    <link:label id="lab_codi_ActualSecuredDebtToEbitdaRatio_019b0d9b-5529-7a94-8252-71861c7677f2_terseLabel_en-US" xlink:label="lab_codi_ActualSecuredDebtToEbitdaRatio" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Actual Secured Debt To Ebitda Ratio</link:label>
    <link:label id="lab_codi_ActualSecuredDebtToEbitdaRatio_label_en-US" xlink:label="lab_codi_ActualSecuredDebtToEbitdaRatio" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Actual Secured Debt To Ebitda Ratio</link:label>
    <link:label id="lab_codi_ActualSecuredDebtToEbitdaRatio_documentation_en-US" xlink:label="lab_codi_ActualSecuredDebtToEbitdaRatio" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Actual Secured Debt To Ebitda Ratio</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_codi_ActualSecuredDebtToEbitdaRatio" xlink:href="codi-20250331.xsd#codi_ActualSecuredDebtToEbitdaRatio"/>
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    <link:label id="lab_us-gaap_AccountsReceivableNet_a94feedc-42f0-4f4b-acdc-b351371a10bd_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>
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    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AccountsReceivableNet" xlink:to="lab_us-gaap_AccountsReceivableNet" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_PropertyPlantAndEquipmentAbstract_e79e9607-5062-459b-9f64-f35b23ee23ec_terseLabel_en-US" xlink:label="lab_us-gaap_PropertyPlantAndEquipmentAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Property, Plant and Equipment [Abstract]</link:label>
    <link:label id="lab_us-gaap_PropertyPlantAndEquipmentAbstract_label_en-US" xlink:label="lab_us-gaap_PropertyPlantAndEquipmentAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Property, Plant and Equipment [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PropertyPlantAndEquipmentAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_PropertyPlantAndEquipmentAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PropertyPlantAndEquipmentAbstract" xlink:to="lab_us-gaap_PropertyPlantAndEquipmentAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_EntityRegistrantName_e05d21cc-980e-415b-a6db-99321633ba51_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/2025/dei-2025.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_us-gaap_NatureOfExpenseAxis_984b0293-97e4-4940-9a9c-bbb3efbee789_terseLabel_en-US" xlink:label="lab_us-gaap_NatureOfExpenseAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Nature of Expense [Axis]</link:label>
    <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>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_NatureOfExpenseAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_NatureOfExpenseAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_NatureOfExpenseAxis" xlink:to="lab_us-gaap_NatureOfExpenseAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_codi_TheHoneyPotMember_7a528da9-d4bc-476b-8c23-52159cd16ec0_terseLabel_en-US" xlink:label="lab_codi_TheHoneyPotMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">The Honey Pot</link:label>
    <link:label id="lab_codi_TheHoneyPotMember_label_en-US" xlink:label="lab_codi_TheHoneyPotMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">The Honey Pot [Member]</link:label>
    <link:label id="lab_codi_TheHoneyPotMember_documentation_en-US" xlink:label="lab_codi_TheHoneyPotMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">The Honey Pot</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_codi_TheHoneyPotMember" xlink:href="codi-20250331.xsd#codi_TheHoneyPotMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_codi_TheHoneyPotMember" xlink:to="lab_codi_TheHoneyPotMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DefinedBenefitPlanNetPeriodicBenefitCost_6734e65a-289e-484f-a9c6-ffed4e8e2a9d_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_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/2025/elts/us-gaap-2025.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_us-gaap_RelatedPartyTransactionLineItems_109edef4-f170-46a5-b35d-aac4755c3401_terseLabel_en-US" xlink:label="lab_us-gaap_RelatedPartyTransactionLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Related Party Transaction [Line Items]</link:label>
    <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>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_RelatedPartyTransactionLineItems" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_RelatedPartyTransactionLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_RelatedPartyTransactionLineItems" xlink:to="lab_us-gaap_RelatedPartyTransactionLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OtherSignificantNoncashTransactionValueOfConsiderationReceived1_019b0d86-95b5-7c9a-a4d6-d7438449e4ea_terseLabel_en-US" xlink:label="lab_us-gaap_OtherSignificantNoncashTransactionValueOfConsiderationReceived1" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Other Significant Noncash Transaction, Value of Consideration Received</link:label>
    <link:label id="lab_us-gaap_OtherSignificantNoncashTransactionValueOfConsiderationReceived1_label_en-US" xlink:label="lab_us-gaap_OtherSignificantNoncashTransactionValueOfConsiderationReceived1" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Other Significant Noncash Transaction, Value of Consideration Received</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OtherSignificantNoncashTransactionValueOfConsiderationReceived1" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_OtherSignificantNoncashTransactionValueOfConsiderationReceived1"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OtherSignificantNoncashTransactionValueOfConsiderationReceived1" xlink:to="lab_us-gaap_OtherSignificantNoncashTransactionValueOfConsiderationReceived1" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_DocumentQuarterlyReport_045551ec-2d9d-4ef7-96c1-14f8ff2b8e6d_terseLabel_en-US" xlink:label="lab_dei_DocumentQuarterlyReport" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Document Quarterly Report</link:label>
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    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_DocumentQuarterlyReport" xlink:to="lab_dei_DocumentQuarterlyReport" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DeferredIncomeTaxesAndTaxCredits_0e6929f2-acda-4e5f-a8e1-7ff7f6f0db80_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 income 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/2025/elts/us-gaap-2025.xsd#us-gaap_DeferredIncomeTaxesAndTaxCredits"/>
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    <link:label id="lab_us-gaap_LongTermDebtFairValue_4d6f946a-3300-4a86-a832-5b23b24ae7ca_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/2025/elts/us-gaap-2025.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_srt_RestatementDomain_a6e25d00-de67-44c6-a28b-dfa37800428a_terseLabel_en-US" xlink:label="lab_srt_RestatementDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Revision of Prior Period [Domain]</link:label>
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    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_srt_RestatementDomain" xlink:to="lab_srt_RestatementDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearTwo_4c9005fd-a7c2-4072-924b-45d3c546659d_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">2020</link:label>
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    <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_ScheduleOfDebtTableTextBlock_be653e42-d1b9-477c-8b21-8f7e5adee009_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfDebtTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Summary of Debt Holdings</link:label>
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    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ScheduleOfDebtTableTextBlock" xlink:to="lab_us-gaap_ScheduleOfDebtTableTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_MachineryAndEquipmentMember_c2296297-fede-4fd5-8592-ac2f4f94d1d8_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/2025/elts/us-gaap-2025.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_RelatedPartyTransactionsByRelatedPartyAxis_8032ec09-5c4b-4ff5-8f6f-d6a984f2c96a_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>
    <link:label id="lab_us-gaap_RelatedPartyTransactionsByRelatedPartyAxis_label_en-US" xlink:label="lab_us-gaap_RelatedPartyTransactionsByRelatedPartyAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Related and Nonrelated Parties [Axis]</link:label>
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    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_RelatedPartyTransactionsByRelatedPartyAxis" xlink:to="lab_us-gaap_RelatedPartyTransactionsByRelatedPartyAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DefinedBenefitPlanInterestCost_533dce87-45ab-4470-9a7b-04ba44267049_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/2025/elts/us-gaap-2025.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_MaterialReconcilingItemsMember_13f4c6fb-c541-417d-af90-46771ef11f42_terseLabel_en-US" xlink:label="lab_us-gaap_MaterialReconcilingItemsMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Reconciliation of Segment to Consolidated</link:label>
    <link:label id="lab_us-gaap_MaterialReconcilingItemsMember_label_en-US" xlink:label="lab_us-gaap_MaterialReconcilingItemsMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Segment Reporting, Reconciling Item, Excluding Corporate Nonsegment [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_MaterialReconcilingItemsMember" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_MaterialReconcilingItemsMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_MaterialReconcilingItemsMember" xlink:to="lab_us-gaap_MaterialReconcilingItemsMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OtherOwnershipInterestsNameDomain_4af88c49-63f8-4735-a965-fb3e941782ba_terseLabel_en-US" xlink:label="lab_us-gaap_OtherOwnershipInterestsNameDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Other Ownership Interests, Name [Domain]</link:label>
    <link:label id="lab_us-gaap_OtherOwnershipInterestsNameDomain_label_en-US" xlink:label="lab_us-gaap_OtherOwnershipInterestsNameDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Other Ownership Interests, Name [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OtherOwnershipInterestsNameDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_OtherOwnershipInterestsNameDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OtherOwnershipInterestsNameDomain" xlink:to="lab_us-gaap_OtherOwnershipInterestsNameDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_NumberOfStores_4ce03baf-e53a-48b2-846e-861f78f8c89c_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>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_NumberOfStores" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_NumberOfStores"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_NumberOfStores" xlink:to="lab_us-gaap_NumberOfStores" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_NetCashProvidedByUsedInOperatingActivitiesContinuingOperations_752b0d4f-18f3-4d8d-a4c3-44861756ddce_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">Cash used in operating activities - continuing operations</link:label>
    <link:label id="lab_us-gaap_NetCashProvidedByUsedInOperatingActivitiesContinuingOperations_label_en-US" xlink:label="lab_us-gaap_NetCashProvidedByUsedInOperatingActivitiesContinuingOperations" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Cash Provided by (Used in) Operating Activity, Continuing Operation</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_NetCashProvidedByUsedInOperatingActivitiesContinuingOperations" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_NetCashProvidedByUsedInOperatingActivitiesContinuingOperations"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_NetCashProvidedByUsedInOperatingActivitiesContinuingOperations" xlink:to="lab_us-gaap_NetCashProvidedByUsedInOperatingActivitiesContinuingOperations" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OtherNoncurrentLiabilitiesMember_77dce144-c180-4b40-bc12-4c785d0ef98f_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">Other Noncurrent Liabilities [Member]</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/2025/elts/us-gaap-2025.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_RepaymentsOfLongTermLinesOfCredit_7d7daa9d-b9ed-4477-904d-95c2074ec2da_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 - revolving 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/2025/elts/us-gaap-2025.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_us-gaap_LettersOfCreditOutstandingAmount_055bef3b-f8c6-4676-94cd-7c7437423d35_terseLabel_en-US" xlink:label="lab_us-gaap_LettersOfCreditOutstandingAmount" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Letter of credit outstanding</link:label>
    <link:label id="lab_us-gaap_LettersOfCreditOutstandingAmount_label_en-US" xlink:label="lab_us-gaap_LettersOfCreditOutstandingAmount" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Letters of Credit Outstanding, Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LettersOfCreditOutstandingAmount" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_LettersOfCreditOutstandingAmount"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LettersOfCreditOutstandingAmount" xlink:to="lab_us-gaap_LettersOfCreditOutstandingAmount" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DiscontinuedOperationGainLossOnDisposalOfDiscontinuedOperationNetOfTax_6d045817-a11b-4fd4-8ef5-c73bb4870da5_terseLabel_en-US" xlink:label="lab_us-gaap_DiscontinuedOperationGainLossOnDisposalOfDiscontinuedOperationNetOfTax" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Gain on sale of discontinued operations, net of income tax</link:label>
    <link:label id="lab_us-gaap_DiscontinuedOperationGainLossOnDisposalOfDiscontinuedOperationNetOfTax_label_en-US" xlink:label="lab_us-gaap_DiscontinuedOperationGainLossOnDisposalOfDiscontinuedOperationNetOfTax" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Discontinued Operation, Gain (Loss) on Disposal of Discontinued Operation, Net of Tax</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DiscontinuedOperationGainLossOnDisposalOfDiscontinuedOperationNetOfTax" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DiscontinuedOperationGainLossOnDisposalOfDiscontinuedOperationNetOfTax"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DiscontinuedOperationGainLossOnDisposalOfDiscontinuedOperationNetOfTax" xlink:to="lab_us-gaap_DiscontinuedOperationGainLossOnDisposalOfDiscontinuedOperationNetOfTax" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_NetCashProvidedByUsedInInvestingActivitiesContinuingOperations_6a8e23f3-887c-4983-8238-ee010bfc1837_totalLabel_en-US" xlink:label="lab_us-gaap_NetCashProvidedByUsedInInvestingActivitiesContinuingOperations" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Cash used in investing activities - continuing operations</link:label>
    <link:label id="lab_us-gaap_NetCashProvidedByUsedInInvestingActivitiesContinuingOperations_label_en-US" xlink:label="lab_us-gaap_NetCashProvidedByUsedInInvestingActivitiesContinuingOperations" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Cash Provided by (Used in) Investing Activity, Continuing Operation</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_NetCashProvidedByUsedInInvestingActivitiesContinuingOperations" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_NetCashProvidedByUsedInInvestingActivitiesContinuingOperations"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_NetCashProvidedByUsedInInvestingActivitiesContinuingOperations" xlink:to="lab_us-gaap_NetCashProvidedByUsedInInvestingActivitiesContinuingOperations" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ProceedsFromPaymentsForOtherFinancingActivities_9d367998-18b3-4193-9a54-a4d6da8cb112_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_ProceedsFromPaymentsForOtherFinancingActivities" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" 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 (Payment for) Other Financing Activity</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ProceedsFromPaymentsForOtherFinancingActivities" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ProceedsFromPaymentsForOtherFinancingActivities"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ProceedsFromPaymentsForOtherFinancingActivities" xlink:to="lab_us-gaap_ProceedsFromPaymentsForOtherFinancingActivities" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_PreferredStockDividendRatePercentage_39b44152-15f3-4afd-9afb-2654124b2f55_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/2025/elts/us-gaap-2025.xsd#us-gaap_PreferredStockDividendRatePercentage"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PreferredStockDividendRatePercentage" xlink:to="lab_us-gaap_PreferredStockDividendRatePercentage" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_BusinessAcquisitionProFormaInformationNonrecurringAdjustmentsTable_79477956-a358-4370-b3ad-55ac9e814975_terseLabel_en-US" xlink:label="lab_us-gaap_BusinessAcquisitionProFormaInformationNonrecurringAdjustmentsTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Business Combination, Pro Forma Information [Table]</link:label>
    <link:label id="lab_us-gaap_BusinessAcquisitionProFormaInformationNonrecurringAdjustmentsTable_label_en-US" xlink:label="lab_us-gaap_BusinessAcquisitionProFormaInformationNonrecurringAdjustmentsTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Business Combination, Pro Forma Information [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_BusinessAcquisitionProFormaInformationNonrecurringAdjustmentsTable" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_BusinessAcquisitionProFormaInformationNonrecurringAdjustmentsTable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_BusinessAcquisitionProFormaInformationNonrecurringAdjustmentsTable" xlink:to="lab_us-gaap_BusinessAcquisitionProFormaInformationNonrecurringAdjustmentsTable" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedLiabilitiesAbstract_6840a6c1-99fb-428a-a418-de47d7badc7c_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 Liability Assumed, Liability [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedLiabilitiesAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedLiabilitiesAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedLiabilitiesAbstract" xlink:to="lab_us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedLiabilitiesAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_SubsidiarySaleOfStockAxis_be046163-aec2-4062-bc58-e4dddc561dd5_terseLabel_en-US" xlink:label="lab_us-gaap_SubsidiarySaleOfStockAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Sale of Stock [Axis]</link:label>
    <link:label id="lab_us-gaap_SubsidiarySaleOfStockAxis_label_en-US" xlink:label="lab_us-gaap_SubsidiarySaleOfStockAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Sale of Stock [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SubsidiarySaleOfStockAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_SubsidiarySaleOfStockAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_SubsidiarySaleOfStockAxis" xlink:to="lab_us-gaap_SubsidiarySaleOfStockAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_SegmentReportingRevenueReconcilingItemLineItems_612f07fa-ca81-4bc7-b4c8-897e08f7a7c2_terseLabel_en-US" xlink:label="lab_us-gaap_SegmentReportingRevenueReconcilingItemLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Segment Reporting, Revenue Reconciling Item [Line Items]</link:label>
    <link:label id="lab_us-gaap_SegmentReportingRevenueReconcilingItemLineItems_label_en-US" xlink:label="lab_us-gaap_SegmentReportingRevenueReconcilingItemLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Segment Reporting, Revenue Reconciling Item [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SegmentReportingRevenueReconcilingItemLineItems" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_SegmentReportingRevenueReconcilingItemLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_SegmentReportingRevenueReconcilingItemLineItems" xlink:to="lab_us-gaap_SegmentReportingRevenueReconcilingItemLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_codi_ErgobabyMember_a6c3889f-0920-4778-8bab-0c443055ba78_terseLabel_en-US" xlink:label="lab_codi_ErgobabyMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Ergobaby [Member]</link:label>
    <link:label id="lab_codi_ErgobabyMember_label_en-US" xlink:label="lab_codi_ErgobabyMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Ergobaby [Member]</link:label>
    <link:label id="lab_codi_ErgobabyMember_documentation_en-US" xlink:label="lab_codi_ErgobabyMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Ergobaby.</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_codi_ErgobabyMember" xlink:href="codi-20250331.xsd#codi_ErgobabyMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_codi_ErgobabyMember" xlink:to="lab_codi_ErgobabyMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AssetsOfDisposalGroupIncludingDiscontinuedOperationAbstract_19c4379b-efb3-4634-bf7b-e2a44e06aa2d_terseLabel_en-US" xlink:label="lab_us-gaap_AssetsOfDisposalGroupIncludingDiscontinuedOperationAbstract" 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_AssetsOfDisposalGroupIncludingDiscontinuedOperationAbstract_label_en-US" xlink:label="lab_us-gaap_AssetsOfDisposalGroupIncludingDiscontinuedOperationAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Disposal Group, Including Discontinued Operation, Assets [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AssetsOfDisposalGroupIncludingDiscontinuedOperationAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_AssetsOfDisposalGroupIncludingDiscontinuedOperationAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AssetsOfDisposalGroupIncludingDiscontinuedOperationAbstract" xlink:to="lab_us-gaap_AssetsOfDisposalGroupIncludingDiscontinuedOperationAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_codi_DistributionToShareholders_838bdee9-aef4-4e8f-bd2e-867f3be97462_negatedLabel_en-US" xlink:label="lab_codi_DistributionToShareholders" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:type="resource" xml:lang="en-US">Distribution To Shareholders</link:label>
    <link:label id="lab_codi_DistributionToShareholders_202302e1-134c-4bfa-b914-d7dcfb4a4e7f_verboseLabel_en-US" xlink:label="lab_codi_DistributionToShareholders" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Distribution To Shareholders</link:label>
    <link:label id="lab_codi_DistributionToShareholders_1109738a-5958-4bbf-93c1-d731b5c20dbe_terseLabel_en-US" xlink:label="lab_codi_DistributionToShareholders" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Cash distributions funded by debt</link:label>
    <link:label id="lab_codi_DistributionToShareholders_label_en-US" xlink:label="lab_codi_DistributionToShareholders" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Distribution To Shareholders</link:label>
    <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>
    <link:loc xlink:type="locator" xlink:label="loc_codi_DistributionToShareholders" xlink:href="codi-20250331.xsd#codi_DistributionToShareholders"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_codi_DistributionToShareholders" xlink:to="lab_codi_DistributionToShareholders" xlink:type="arc" order="1"/>
    <link:label id="lab_srt_ScenarioPreviouslyReportedMember_019b0dbc-223f-7e2b-8b82-f20f8523336d_terseLabel_en-US" xlink:label="lab_srt_ScenarioPreviouslyReportedMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Previously Reported</link:label>
    <link:label id="lab_srt_ScenarioPreviouslyReportedMember_label_en-US" xlink:label="lab_srt_ScenarioPreviouslyReportedMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Previously Reported [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_srt_ScenarioPreviouslyReportedMember" xlink:href="https://xbrl.fasb.org/srt/2025/elts/srt-2025.xsd#srt_ScenarioPreviouslyReportedMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_srt_ScenarioPreviouslyReportedMember" xlink:to="lab_srt_ScenarioPreviouslyReportedMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueNextTwelveMonths_48ccc3f5-78c2-46e0-911a-a518d0659592_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">Lessee, Operating Lease, Liability, to be Paid, Year One</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>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueNextTwelveMonths" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueNextTwelveMonths"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueNextTwelveMonths" xlink:to="lab_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueNextTwelveMonths" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_MinorityInterest_892b1994-ee3f-45a0-9986-a8dc19a93a95_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_bfd32fb6-01a3-4a37-b6b6-4ac03184d77a_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">Noncontrolling interest of discontinued operations</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/2025/elts/us-gaap-2025.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_us-gaap_LeaseholdImprovementsMember_85ac495b-aa7e-43ab-a6c3-2e25b56653e7_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/2025/elts/us-gaap-2025.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_ReconciliationOfRevenueFromSegmentsToConsolidatedTable_1f9142c0-6a6f-4c5b-91d8-669f9970184b_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/2025/elts/us-gaap-2025.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_OtherNoncashIncomeExpense_0d5c341f-221f-428d-93c9-1263a08be255_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>
    <link:label id="lab_us-gaap_OtherNoncashIncomeExpense_label_en-US" xlink:label="lab_us-gaap_OtherNoncashIncomeExpense" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Other Noncash Income (Expense)</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OtherNoncashIncomeExpense" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_OtherNoncashIncomeExpense"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OtherNoncashIncomeExpense" xlink:to="lab_us-gaap_OtherNoncashIncomeExpense" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DisaggregationOfRevenueLineItems_a0a94cc9-9ebb-422e-81a8-482945efe6b0_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/2025/elts/us-gaap-2025.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_DiscontinuedOperationsDisposedOfBySaleMember_616ca54f-7d60-4bcd-b154-a7d3dddafb96_verboseLabel_en-US" xlink:label="lab_us-gaap_DiscontinuedOperationsDisposedOfBySaleMember" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Discontinued Operations, Disposed of by Sale</link:label>
    <link:label id="lab_us-gaap_DiscontinuedOperationsDisposedOfBySaleMember_9d2fc58f-7300-4774-9939-6ba9ff0ae0b8_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 [Member]</link:label>
    <link:label id="lab_us-gaap_DiscontinuedOperationsDisposedOfBySaleMember_label_en-US" xlink:label="lab_us-gaap_DiscontinuedOperationsDisposedOfBySaleMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Discontinued Operations, Disposed of by Sale [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DiscontinuedOperationsDisposedOfBySaleMember" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DiscontinuedOperationsDisposedOfBySaleMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DiscontinuedOperationsDisposedOfBySaleMember" xlink:to="lab_us-gaap_DiscontinuedOperationsDisposedOfBySaleMember" xlink:type="arc" order="1"/>
    <link:label id="lab_codi_SeasonalityPolicyTextBlock_a2ce1ffd-ddbd-4238-bdd4-0fe6e733c2b2_terseLabel_en-US" xlink:label="lab_codi_SeasonalityPolicyTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Seasonality</link:label>
    <link:label id="lab_codi_SeasonalityPolicyTextBlock_label_en-US" xlink:label="lab_codi_SeasonalityPolicyTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Seasonality [Policy Text Block]</link:label>
    <link:label id="lab_codi_SeasonalityPolicyTextBlock_documentation_en-US" xlink:label="lab_codi_SeasonalityPolicyTextBlock" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Seasonality [Policy Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_codi_SeasonalityPolicyTextBlock" xlink:href="codi-20250331.xsd#codi_SeasonalityPolicyTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_codi_SeasonalityPolicyTextBlock" xlink:to="lab_codi_SeasonalityPolicyTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DebtInstrumentFaceAmount_bfae4558-bc72-47ef-b272-9257320125d8_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">Credit facility obtained</link:label>
    <link:label id="lab_us-gaap_DebtInstrumentFaceAmount_ec296d3a-1312-46ff-ad5b-fb456201ef0e_verboseLabel_en-US" xlink:label="lab_us-gaap_DebtInstrumentFaceAmount" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Debt instrument</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/2025/elts/us-gaap-2025.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_codi_InterestPIKPayment_019b23a5-46c6-7b33-8589-12e9743c5834_terseLabel_en-US" xlink:label="lab_codi_InterestPIKPayment" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Interest PIK Payment</link:label>
    <link:label id="lab_codi_InterestPIKPayment_label_en-US" xlink:label="lab_codi_InterestPIKPayment" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Interest PIK Payment</link:label>
    <link:label id="lab_codi_InterestPIKPayment_documentation_en-US" xlink:label="lab_codi_InterestPIKPayment" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Interest PIK Payment</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_codi_InterestPIKPayment" xlink:href="codi-20250331.xsd#codi_InterestPIKPayment"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_codi_InterestPIKPayment" xlink:to="lab_codi_InterestPIKPayment" xlink:type="arc" order="1"/>
    <link:label id="lab_codi_ExcessOfProjectedCashDisbursements_019b23a8-d674-7cbc-9aa5-ac47c2fbd3a2_terseLabel_en-US" xlink:label="lab_codi_ExcessOfProjectedCashDisbursements" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Excess of projected cash disbursements</link:label>
    <link:label id="lab_codi_ExcessOfProjectedCashDisbursements_label_en-US" xlink:label="lab_codi_ExcessOfProjectedCashDisbursements" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Excess of projected cash disbursements</link:label>
    <link:label id="lab_codi_ExcessOfProjectedCashDisbursements_documentation_en-US" xlink:label="lab_codi_ExcessOfProjectedCashDisbursements" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Excess of projected cash disbursements</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_codi_ExcessOfProjectedCashDisbursements" xlink:href="codi-20250331.xsd#codi_ExcessOfProjectedCashDisbursements"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_codi_ExcessOfProjectedCashDisbursements" xlink:to="lab_codi_ExcessOfProjectedCashDisbursements" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_SubsegmentsDomain_55ffc48c-a06f-40ed-a237-24a0bea63780_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/2025/elts/us-gaap-2025.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_DebtInstrumentNameDomain_9c3c096d-e8b5-428b-92de-1b16f6b2f149_terseLabel_en-US" xlink:label="lab_us-gaap_DebtInstrumentNameDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Debt Instrument, Name [Domain]</link:label>
    <link:label id="lab_us-gaap_DebtInstrumentNameDomain_label_en-US" xlink:label="lab_us-gaap_DebtInstrumentNameDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Instrument, Name [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtInstrumentNameDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DebtInstrumentNameDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DebtInstrumentNameDomain" xlink:to="lab_us-gaap_DebtInstrumentNameDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_StatementOfIncomeAndComprehensiveIncomeAbstract_fbff1ed2-88a3-437a-b74d-7f67211c2214_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/2025/elts/us-gaap-2025.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_OperatingCostsAndExpenses_0cc96832-5ff7-4c90-b7fa-9d9a127db0bf_terseLabel_en-US" xlink:label="lab_us-gaap_OperatingCostsAndExpenses" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Operating Costs and Expenses</link:label>
    <link:label id="lab_us-gaap_OperatingCostsAndExpenses_label_en-US" xlink:label="lab_us-gaap_OperatingCostsAndExpenses" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Operating Costs and Expenses</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OperatingCostsAndExpenses" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_OperatingCostsAndExpenses"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OperatingCostsAndExpenses" xlink:to="lab_us-gaap_OperatingCostsAndExpenses" xlink:type="arc" order="1"/>
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    <link:label id="lab_us-gaap_GoodwillMember_5aa5d461-a6d9-4848-871e-721d852987a7_terseLabel_en-US" xlink:label="lab_us-gaap_GoodwillMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Goodwill [Member]</link:label>
    <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>
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    <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>
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    <link:label id="lab_us-gaap_EffectiveIncomeTaxRateReconciliationForeignIncomeTaxRateDifferential_07d2b022-1077-41fa-855b-b21b5c3ebca6_terseLabel_en-US" xlink:label="lab_us-gaap_EffectiveIncomeTaxRateReconciliationForeignIncomeTaxRateDifferential" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Effective Income Tax Rate Reconciliation, Foreign Income Tax Rate Differential, Percent</link:label>
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    <link:label id="lab_codi_SeriesAPreferredSharesRepresentingSeriesATrustPreferredInterestInCompassDiversifiedHoldingsMember_615b0cb4-9987-4120-9424-5a6542aa9df2_terseLabel_en-US" xlink:label="lab_codi_SeriesAPreferredSharesRepresentingSeriesATrustPreferredInterestInCompassDiversifiedHoldingsMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Series A Preferred Shares representing Series A Trust Preferred Interest in Compass Diversified Holdings</link:label>
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    <link:label id="lab_us-gaap_OtherComprehensiveIncomeLossNetOfTaxPortionAttributableToNoncontrollingInterest_563a53ac-c506-4c0c-8e3c-2e1bbf6bb27e_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 loss attributable to noncontrolling interests</link:label>
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    <link:label id="lab_codi_PreferredStockCashDistributionsPaidPerShare_147a7e6c-7809-4026-83e4-fe78b963b0f8_terseLabel_en-US" xlink:label="lab_codi_PreferredStockCashDistributionsPaidPerShare" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Preferred Stock, Cash Distributions Paid, Per Share</link:label>
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    <link:label id="lab_us-gaap_AccumulatedOtherComprehensiveIncomeLossNetOfTax_e9d3b30b-353e-473e-94f7-f1e0751f874d_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 loss</link:label>
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    <link:label id="lab_us-gaap_GoodwillGross_f20ad79f-cbb4-4d2d-bad8-52d276f9a8f7_terseLabel_en-US" xlink:label="lab_us-gaap_GoodwillGross" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Goodwill - gross carrying amount</link:label>
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    <link:label id="lab_codi_BusinessCombinationStepAcquisitionInventoryRemeasurement_69e5752b-81e4-45cc-a90e-2f94addfeef1_terseLabel_en-US" xlink:label="lab_codi_BusinessCombinationStepAcquisitionInventoryRemeasurement" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Business Combination, Step Acquisition, Inventory, Remeasurement</link:label>
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    <link:label id="lab_codi_NetIncomeLossAvailableToTrustStockNetOfHoldingEventAdjustment_2f974c90-1af8-4e98-aa7f-55b6405c6d06_terseLabel_en-US" xlink:label="lab_codi_NetIncomeLossAvailableToTrustStockNetOfHoldingEventAdjustment" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Net income (loss) from continuing operations attributable to common shares of Holdings</link:label>
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    <link:label id="lab_us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInNextTwelveMonths_3d9362f0-7fee-4dbf-82de-312e45d41f86_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>
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    <link:label id="lab_us-gaap_IndefiniteLivedTradeNames_68437d24-f044-42ef-afc9-e53672dd3437_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/2025/elts/us-gaap-2025.xsd#us-gaap_IndefiniteLivedTradeNames"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_IndefiniteLivedTradeNames" xlink:to="lab_us-gaap_IndefiniteLivedTradeNames" xlink:type="arc" order="1"/>
    <link:label id="lab_srt_LitigationCaseAxis_019b0da3-0fb0-7010-bb75-fa6a883044f6_terseLabel_en-US" xlink:label="lab_srt_LitigationCaseAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Litigation Case [Axis]</link:label>
    <link:label id="lab_srt_LitigationCaseAxis_label_en-US" xlink:label="lab_srt_LitigationCaseAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Litigation Case [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_srt_LitigationCaseAxis" xlink:href="https://xbrl.fasb.org/srt/2025/elts/srt-2025.xsd#srt_LitigationCaseAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_srt_LitigationCaseAxis" xlink:to="lab_srt_LitigationCaseAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_SegmentDomain_bc03feeb-59d7-4141-ace6-ecf485757a9b_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_299d7351-2e10-44a1-b278-2c897b47ca89_verboseLabel_en-US" xlink:label="lab_us-gaap_SegmentDomain" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Segment [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/2025/elts/us-gaap-2025.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_IncomeStatementLocationAxis_6285a855-145a-48df-b39d-8250659308ab_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>
    <link:label id="lab_us-gaap_IncomeStatementLocationAxis_label_en-US" xlink:label="lab_us-gaap_IncomeStatementLocationAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Statement of Income Location, Balance [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncomeStatementLocationAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_IncomeStatementLocationAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_IncomeStatementLocationAxis" xlink:to="lab_us-gaap_IncomeStatementLocationAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInYearFive_9f638fee-8e7d-4f69-87bb-a0132793215e_terseLabel_en-US" xlink:label="lab_us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInYearFive" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Long-Term Debt, Maturity, Year Five</link:label>
    <link:label id="lab_us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInYearFive_label_en-US" xlink:label="lab_us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInYearFive" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Long-Term Debt, Maturity, Year Five</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInYearFive" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInYearFive"/>
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    <link:label id="lab_codi_LifoamMember_87013b99-73bb-4a8b-b094-ab45eae0f05f_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-20250331.xsd#codi_LifoamMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_codi_LifoamMember" xlink:to="lab_codi_LifoamMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_PaymentsForCommissions_9ff36313-6651-46d3-991f-6f23369e6bd0_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/2025/elts/us-gaap-2025.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_us-gaap_FairValueMeasurementsFairValueHierarchyDomain_30dd2117-68aa-4aa3-b689-941e05b8f0b3_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/2025/elts/us-gaap-2025.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_us-gaap_LiabilitiesOfDisposalGroupIncludingDiscontinuedOperationAbstract_9798f59a-bb97-4d87-b604-6edc218bfb15_terseLabel_en-US" xlink:label="lab_us-gaap_LiabilitiesOfDisposalGroupIncludingDiscontinuedOperationAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Liabilities:</link:label>
    <link:label id="lab_us-gaap_LiabilitiesOfDisposalGroupIncludingDiscontinuedOperationAbstract_label_en-US" xlink:label="lab_us-gaap_LiabilitiesOfDisposalGroupIncludingDiscontinuedOperationAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Disposal Group, Including Discontinued Operation, Liabilities [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LiabilitiesOfDisposalGroupIncludingDiscontinuedOperationAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_LiabilitiesOfDisposalGroupIncludingDiscontinuedOperationAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LiabilitiesOfDisposalGroupIncludingDiscontinuedOperationAbstract" xlink:to="lab_us-gaap_LiabilitiesOfDisposalGroupIncludingDiscontinuedOperationAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_codi_NumberOfClients_35936152-ac6e-4a64-994b-b3213e887018_terseLabel_en-US" xlink:label="lab_codi_NumberOfClients" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Number of clients</link:label>
    <link:label id="lab_codi_NumberOfClients_label_en-US" xlink:label="lab_codi_NumberOfClients" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Number Of Clients</link:label>
    <link:label id="lab_codi_NumberOfClients_documentation_en-US" xlink:label="lab_codi_NumberOfClients" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Number of clients.</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_codi_NumberOfClients" xlink:href="codi-20250331.xsd#codi_NumberOfClients"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_codi_NumberOfClients" xlink:to="lab_codi_NumberOfClients" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_BalanceSheetLocationDomain_65fa89c2-c67a-4d8d-8f16-81a0e6980534_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">Balance Sheet Location [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/2025/elts/us-gaap-2025.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_IncreaseDecreaseInInventories_e7e79045-f0bf-4e5e-b2cd-c6faab7b8520_negatedLabel_en-US" xlink:label="lab_us-gaap_IncreaseDecreaseInInventories" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:type="resource" xml:lang="en-US">Inventories</link:label>
    <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>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncreaseDecreaseInInventories" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_IncreaseDecreaseInInventories"/>
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    <link:label id="lab_us-gaap_InventoryNet_68a99363-679d-4fb5-8c7e-7bc749168e81_terseLabel_en-US" xlink:label="lab_us-gaap_InventoryNet" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Inventories, net</link:label>
    <link:label id="lab_us-gaap_InventoryNet_ab03927a-5358-4781-8c9e-a6b35ba5c0bf_totalLabel_en-US" xlink:label="lab_us-gaap_InventoryNet" 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_InventoryNet_label_en-US" xlink:label="lab_us-gaap_InventoryNet" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Inventory, Net</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_InventoryNet" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_InventoryNet"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_InventoryNet" xlink:to="lab_us-gaap_InventoryNet" xlink:type="arc" order="1"/>
    <link:label id="lab_codi_LLCSubsidiariesMember_019b14ad-db21-79e5-bf47-c7694d9bf082_terseLabel_en-US" xlink:label="lab_codi_LLCSubsidiariesMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">LLC Subsidiaries</link:label>
    <link:label id="lab_codi_LLCSubsidiariesMember_label_en-US" xlink:label="lab_codi_LLCSubsidiariesMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">LLC Subsidiaries [Member]</link:label>
    <link:label id="lab_codi_LLCSubsidiariesMember_documentation_en-US" xlink:label="lab_codi_LLCSubsidiariesMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">LLC Subsidiaries</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_codi_LLCSubsidiariesMember" xlink:href="codi-20250331.xsd#codi_LLCSubsidiariesMember"/>
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    <link:label id="lab_us-gaap_AmortizationOfFinancingCostsAndDiscounts_f2118d3c-58df-45c5-b008-e768227068e0_terseLabel_en-US" xlink:label="lab_us-gaap_AmortizationOfFinancingCostsAndDiscounts" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Amortization of debt issuance costs</link:label>
    <link:label id="lab_us-gaap_AmortizationOfFinancingCostsAndDiscounts_label_en-US" xlink:label="lab_us-gaap_AmortizationOfFinancingCostsAndDiscounts" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Amortization of Debt Issuance Costs and Discounts</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AmortizationOfFinancingCostsAndDiscounts" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_AmortizationOfFinancingCostsAndDiscounts"/>
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    <link:label id="lab_us-gaap_FiniteLivedIntangibleAssetsByMajorClassAxis_1666ae8e-2eec-45a6-bd61-3c6928cdb43c_terseLabel_en-US" xlink:label="lab_us-gaap_FiniteLivedIntangibleAssetsByMajorClassAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Finite-Lived Intangible Assets by Major Class [Axis]</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FiniteLivedIntangibleAssetsByMajorClassAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FiniteLivedIntangibleAssetsByMajorClassAxis"/>
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    <link:label id="lab_srt_MinimumMember_c22e02df-1f97-497e-a339-4f85cf160a28_terseLabel_en-US" xlink:label="lab_srt_MinimumMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Minimum</link:label>
    <link:label id="lab_srt_MinimumMember_label_en-US" xlink:label="lab_srt_MinimumMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Minimum [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_srt_MinimumMember" xlink:href="https://xbrl.fasb.org/srt/2025/elts/srt-2025.xsd#srt_MinimumMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_srt_MinimumMember" xlink:to="lab_srt_MinimumMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_IncomeTaxAuthorityNameDomain_4822016d-a614-4343-9d03-76405458496a_terseLabel_en-US" xlink:label="lab_us-gaap_IncomeTaxAuthorityNameDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Income Tax Authority, Name [Domain]</link:label>
    <link:label id="lab_us-gaap_IncomeTaxAuthorityNameDomain_label_en-US" xlink:label="lab_us-gaap_IncomeTaxAuthorityNameDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Income Tax Authority, Name [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncomeTaxAuthorityNameDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_IncomeTaxAuthorityNameDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_IncomeTaxAuthorityNameDomain" xlink:to="lab_us-gaap_IncomeTaxAuthorityNameDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AccumulatedDepreciationDepletionAndAmortizationPropertyPlantAndEquipment_8a119aa4-7559-4451-b4cd-be0e90d8197e_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:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AccumulatedDepreciationDepletionAndAmortizationPropertyPlantAndEquipment" xlink:to="lab_us-gaap_AccumulatedDepreciationDepletionAndAmortizationPropertyPlantAndEquipment" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_GoodwillPurchaseAccountingAdjustments_e2f2a199-9370-40af-8703-8500c24a7e4a_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, Purchase Accounting Adjustments</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/2025/elts/us-gaap-2025.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_DistributionExpenseAllocationInterests_56e168ff-6f53-463b-879e-1a88f9717e41_negatedTerseLabel_en-US" xlink:label="lab_codi_DistributionExpenseAllocationInterests" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Distribution Expense, Allocation Interests</link:label>
    <link:label id="lab_codi_DistributionExpenseAllocationInterests_0b98f419-6c4f-4241-84cd-80d7cad6661d_terseLabel_en-US" xlink:label="lab_codi_DistributionExpenseAllocationInterests" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Distribution Expense, Allocation Interests</link:label>
    <link:label id="lab_codi_DistributionExpenseAllocationInterests_label_en-US" xlink:label="lab_codi_DistributionExpenseAllocationInterests" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Distribution Expense, Allocation Interests</link:label>
    <link:label id="lab_codi_DistributionExpenseAllocationInterests_documentation_en-US" xlink:label="lab_codi_DistributionExpenseAllocationInterests" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Distribution Expense, Allocation Interests</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_codi_DistributionExpenseAllocationInterests" xlink:href="codi-20250331.xsd#codi_DistributionExpenseAllocationInterests"/>
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    <link:label id="lab_codi_ReclassificationOfNoncontrollingInterestToLiability_0c907909-b502-48f1-9770-92d447679603_negatedTerseLabel_en-US" xlink:label="lab_codi_ReclassificationOfNoncontrollingInterestToLiability" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Reclassification of noncontrolling interest to liability</link:label>
    <link:label id="lab_codi_ReclassificationOfNoncontrollingInterestToLiability_label_en-US" xlink:label="lab_codi_ReclassificationOfNoncontrollingInterestToLiability" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Reclassification of noncontrolling interest to liability</link:label>
    <link:label id="lab_codi_ReclassificationOfNoncontrollingInterestToLiability_documentation_en-US" xlink:label="lab_codi_ReclassificationOfNoncontrollingInterestToLiability" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Reclassification of noncontrolling interest to liability</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_codi_ReclassificationOfNoncontrollingInterestToLiability" xlink:href="codi-20250331.xsd#codi_ReclassificationOfNoncontrollingInterestToLiability"/>
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    <link:label id="lab_us-gaap_FairValueDisclosureItemAmountsDomain_89b889b0-ab05-4764-b4e9-75b14ac2efd6_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>
    <link:label id="lab_us-gaap_FairValueDisclosureItemAmountsDomain_label_en-US" xlink:label="lab_us-gaap_FairValueDisclosureItemAmountsDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fair Value Measurement [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueDisclosureItemAmountsDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FairValueDisclosureItemAmountsDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FairValueDisclosureItemAmountsDomain" xlink:to="lab_us-gaap_FairValueDisclosureItemAmountsDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_BusinessAcquisitionsProFormaNetIncomeLoss_4b5e60d6-6870-422f-8586-485337617993_terseLabel_en-US" xlink:label="lab_us-gaap_BusinessAcquisitionsProFormaNetIncomeLoss" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Business Combination, Pro Forma Information, Pro Forma Income (Loss), after Tax</link:label>
    <link:label id="lab_us-gaap_BusinessAcquisitionsProFormaNetIncomeLoss_label_en-US" xlink:label="lab_us-gaap_BusinessAcquisitionsProFormaNetIncomeLoss" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Business Combination, Pro Forma Information, Pro Forma Income (Loss), after Tax</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_BusinessAcquisitionsProFormaNetIncomeLoss" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_BusinessAcquisitionsProFormaNetIncomeLoss"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_BusinessAcquisitionsProFormaNetIncomeLoss" xlink:to="lab_us-gaap_BusinessAcquisitionsProFormaNetIncomeLoss" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_RevenueRecognitionPolicyTextBlock_f4fcf737-a2b1-40f6-b504-ad3f2d58ba57_terseLabel_en-US" xlink:label="lab_us-gaap_RevenueRecognitionPolicyTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Revenue</link:label>
    <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/2025/elts/us-gaap-2025.xsd#us-gaap_RevenueRecognitionPolicyTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_RevenueRecognitionPolicyTextBlock" xlink:to="lab_us-gaap_RevenueRecognitionPolicyTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_SeniorNotesMember_019b234f-8b88-72a6-8c91-698808d17858_terseLabel_en-US" xlink:label="lab_us-gaap_SeniorNotesMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Senior Notes</link:label>
    <link:label id="lab_us-gaap_SeniorNotesMember_label_en-US" xlink:label="lab_us-gaap_SeniorNotesMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Senior Notes [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SeniorNotesMember" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_SeniorNotesMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_SeniorNotesMember" xlink:to="lab_us-gaap_SeniorNotesMember" xlink:type="arc" order="1"/>
    <link:label id="lab_codi_OtherInternationalMember_a526d2d4-9359-4cbf-8c47-fd21c7051311_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-20250331.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_us-gaap_DebtDisclosureTextBlock_a2ff4083-629f-4213-bd2b-f54992758e31_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 Disclosure</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/2025/elts/us-gaap-2025.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_PreferredStockValue_bc86bd5e-031e-483a-ad64-81594014264d_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_96cddc83-03a9-4db7-91c0-db476671c337_verboseLabel_en-US" xlink:label="lab_us-gaap_PreferredStockValue" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Issuance of Trust preferred shares, net of offering costs</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/2025/elts/us-gaap-2025.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_AccountsPayableCurrent_c159e1ed-6fa8-4153-af11-b86046945588_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/2025/elts/us-gaap-2025.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_codi_OperatingAndFinancingLeaseLiabilityToBePaidYearThree_0fe278e1-a263-449a-b8c5-26e39118a738_terseLabel_en-US" xlink:label="lab_codi_OperatingAndFinancingLeaseLiabilityToBePaidYearThree" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Operating and Financing Lease, Liability, to be Paid, Year Three</link:label>
    <link:label id="lab_codi_OperatingAndFinancingLeaseLiabilityToBePaidYearThree_label_en-US" xlink:label="lab_codi_OperatingAndFinancingLeaseLiabilityToBePaidYearThree" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Operating and Financing Lease, Liability, to be Paid, Year Three</link:label>
    <link:label id="lab_codi_OperatingAndFinancingLeaseLiabilityToBePaidYearThree_documentation_en-US" xlink:label="lab_codi_OperatingAndFinancingLeaseLiabilityToBePaidYearThree" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Operating and Financing Lease, Liability, to be Paid, Year Three</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_codi_OperatingAndFinancingLeaseLiabilityToBePaidYearThree" xlink:href="codi-20250331.xsd#codi_OperatingAndFinancingLeaseLiabilityToBePaidYearThree"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_codi_OperatingAndFinancingLeaseLiabilityToBePaidYearThree" xlink:to="lab_codi_OperatingAndFinancingLeaseLiabilityToBePaidYearThree" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OperatingLeasePayments_c8a4fa74-c69c-4bf0-9ebe-052dd5b31631_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 cash flows from operating leases</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/2025/elts/us-gaap-2025.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_us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedLiabilities_f270be01-8082-4983-aa6b-64111b3b551b_terseLabel_en-US" xlink:label="lab_us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedLiabilities" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Business Combination, Recognized Liability Assumed, Liability</link:label>
    <link:label id="lab_us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedLiabilities_label_en-US" xlink:label="lab_us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedLiabilities" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Business Combination, Recognized Liability Assumed, Liability</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedLiabilities" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedLiabilities"/>
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    <link:label id="lab_codi_NumberOfBusinessesOwned_4f86518b-c5fc-42c8-b572-a95e25fca195_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 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-20250331.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_CommonStockValue_c372546f-1c9f-4c96-8718-a0098a216e26_verboseLabel_en-US" xlink:label="lab_us-gaap_CommonStockValue" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" 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 March 31, 2025 and 76,135 issued and $75,236 outstanding at December 31, 2024</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/2025/elts/us-gaap-2025.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_us-gaap_FinanceLeaseRightOfUseAsset_019b23c4-8228-7d8b-8ff5-aa1a74d99637_terseLabel_en-US" xlink:label="lab_us-gaap_FinanceLeaseRightOfUseAsset" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Finance Lease, Right-of-Use Asset, after Accumulated Amortization</link:label>
    <link:label id="lab_us-gaap_FinanceLeaseRightOfUseAsset_label_en-US" xlink:label="lab_us-gaap_FinanceLeaseRightOfUseAsset" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Finance Lease, Right-of-Use Asset, after Accumulated Amortization</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FinanceLeaseRightOfUseAsset" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FinanceLeaseRightOfUseAsset"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FinanceLeaseRightOfUseAsset" xlink:to="lab_us-gaap_FinanceLeaseRightOfUseAsset" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_TaxPeriodAxis_718245ed-e29a-403e-b69e-d988d5024461_terseLabel_en-US" xlink:label="lab_us-gaap_TaxPeriodAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Tax Period [Axis]</link:label>
    <link:label id="lab_us-gaap_TaxPeriodAxis_label_en-US" xlink:label="lab_us-gaap_TaxPeriodAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Tax Period [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_TaxPeriodAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_TaxPeriodAxis"/>
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    <link:label id="lab_us-gaap_GoodwillRollForward_6b2e5b5f-478d-4794-9949-f68454968162_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>
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    <link:label id="lab_us-gaap_AssetsCurrent_3689c248-70b6-49c5-99ee-8b14a18358d8_totalLabel_en-US" xlink:label="lab_us-gaap_AssetsCurrent" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Total current assets</link:label>
    <link:label id="lab_us-gaap_AssetsCurrent_label_en-US" xlink:label="lab_us-gaap_AssetsCurrent" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Assets, Current</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AssetsCurrent" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_AssetsCurrent"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AssetsCurrent" xlink:to="lab_us-gaap_AssetsCurrent" xlink:type="arc" order="1"/>
    <link:label id="lab_srt_RangeAxis_35f5a6f7-fe0c-4522-ab4d-c423070c626f_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>
    <link:label id="lab_srt_RangeAxis_label_en-US" xlink:label="lab_srt_RangeAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Statistical Measurement [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_srt_RangeAxis" xlink:href="https://xbrl.fasb.org/srt/2025/elts/srt-2025.xsd#srt_RangeAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_srt_RangeAxis" xlink:to="lab_srt_RangeAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FinitelivedIntangibleAssetsAcquired1_44040f08-d9c9-47c8-bcb2-16cd353cdc41_terseLabel_en-US" xlink:label="lab_us-gaap_FinitelivedIntangibleAssetsAcquired1" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Finite-lived Intangible Assets Acquired</link:label>
    <link:label id="lab_us-gaap_FinitelivedIntangibleAssetsAcquired1_label_en-US" xlink:label="lab_us-gaap_FinitelivedIntangibleAssetsAcquired1" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Finite-Lived Intangible Assets Acquired</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FinitelivedIntangibleAssetsAcquired1" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FinitelivedIntangibleAssetsAcquired1"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FinitelivedIntangibleAssetsAcquired1" xlink:to="lab_us-gaap_FinitelivedIntangibleAssetsAcquired1" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CashProvidedByUsedInOperatingActivitiesDiscontinuedOperations_36ce7b74-b8a2-4951-8ebe-ced9c1d1cd72_terseLabel_en-US" xlink:label="lab_us-gaap_CashProvidedByUsedInOperatingActivitiesDiscontinuedOperations" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Cash Provided by (Used in) Operating Activity, Discontinued Operation</link:label>
    <link:label id="lab_us-gaap_CashProvidedByUsedInOperatingActivitiesDiscontinuedOperations_label_en-US" xlink:label="lab_us-gaap_CashProvidedByUsedInOperatingActivitiesDiscontinuedOperations" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Cash Provided by (Used in) Operating Activity, Discontinued Operation</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CashProvidedByUsedInOperatingActivitiesDiscontinuedOperations" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_CashProvidedByUsedInOperatingActivitiesDiscontinuedOperations"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CashProvidedByUsedInOperatingActivitiesDiscontinuedOperations" xlink:to="lab_us-gaap_CashProvidedByUsedInOperatingActivitiesDiscontinuedOperations" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DisposalGroupClassificationAxis_98c2518b-6fb5-4c03-8913-5adafc6cc47a_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/2025/elts/us-gaap-2025.xsd#us-gaap_DisposalGroupClassificationAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DisposalGroupClassificationAxis" xlink:to="lab_us-gaap_DisposalGroupClassificationAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_srt_StockRepurchaseProgramAuthorizedAmount1_51b1ed32-44df-49ff-9645-8c5b7bba5178_terseLabel_en-US" xlink:label="lab_srt_StockRepurchaseProgramAuthorizedAmount1" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Stock 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/2025/elts/srt-2025.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_codi_A5.11TacticalMember_bcd8ae7f-1a13-49ff-b00e-39a79fe68c02_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 [Member]</link:label>
    <link:label id="lab_codi_A5.11TacticalMember_label_en-US" xlink:label="lab_codi_A5.11TacticalMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">5.11 Tactical [Member]</link:label>
    <link:label id="lab_codi_A5.11TacticalMember_documentation_en-US" xlink:label="lab_codi_A5.11TacticalMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">5.11 Tactical [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_codi_A5.11TacticalMember" xlink:href="codi-20250331.xsd#codi_A5.11TacticalMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_codi_A5.11TacticalMember" xlink:to="lab_codi_A5.11TacticalMember" xlink:type="arc" order="1"/>
    <link:label id="lab_codi_NonControllingInterestOfDiscontinuedOperationsMember_a64dc850-8014-4a5d-8e98-853c481495c9_terseLabel_en-US" xlink:label="lab_codi_NonControllingInterestOfDiscontinuedOperationsMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Non Controlling Interest Of Discontinued Operations [Member]</link:label>
    <link:label id="lab_codi_NonControllingInterestOfDiscontinuedOperationsMember_label_en-US" xlink:label="lab_codi_NonControllingInterestOfDiscontinuedOperationsMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Non Controlling Interest Of Discontinued Operations [Member]</link:label>
    <link:label id="lab_codi_NonControllingInterestOfDiscontinuedOperationsMember_documentation_en-US" xlink:label="lab_codi_NonControllingInterestOfDiscontinuedOperationsMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Non-controlling interest of discontinued operations.</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_codi_NonControllingInterestOfDiscontinuedOperationsMember" xlink:href="codi-20250331.xsd#codi_NonControllingInterestOfDiscontinuedOperationsMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_codi_NonControllingInterestOfDiscontinuedOperationsMember" xlink:to="lab_codi_NonControllingInterestOfDiscontinuedOperationsMember" xlink:type="arc" order="1"/>
    <link:label id="lab_codi_OperatingAndFinancingLeaseLiabilityToBePaidYearFour_5e7028e5-8f01-4aef-9c6f-8074df38d231_terseLabel_en-US" xlink:label="lab_codi_OperatingAndFinancingLeaseLiabilityToBePaidYearFour" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Operating and Financing Lease, Liability, to be Paid, Year Four</link:label>
    <link:label id="lab_codi_OperatingAndFinancingLeaseLiabilityToBePaidYearFour_label_en-US" xlink:label="lab_codi_OperatingAndFinancingLeaseLiabilityToBePaidYearFour" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Operating and Financing Lease, Liability, to be Paid, Year Four</link:label>
    <link:label id="lab_codi_OperatingAndFinancingLeaseLiabilityToBePaidYearFour_documentation_en-US" xlink:label="lab_codi_OperatingAndFinancingLeaseLiabilityToBePaidYearFour" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Operating and Financing Lease, Liability, to be Paid, Year Four</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_codi_OperatingAndFinancingLeaseLiabilityToBePaidYearFour" xlink:href="codi-20250331.xsd#codi_OperatingAndFinancingLeaseLiabilityToBePaidYearFour"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_codi_OperatingAndFinancingLeaseLiabilityToBePaidYearFour" xlink:to="lab_codi_OperatingAndFinancingLeaseLiabilityToBePaidYearFour" xlink:type="arc" order="1"/>
    <link:label id="lab_codi_SecondForbearanceAgreementMember_019b17df-4264-7f97-afd7-953b16fa58b9_terseLabel_en-US" xlink:label="lab_codi_SecondForbearanceAgreementMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Second Forbearance Agreement</link:label>
    <link:label id="lab_codi_SecondForbearanceAgreementMember_label_en-US" xlink:label="lab_codi_SecondForbearanceAgreementMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Second Forbearance Agreement [Member]</link:label>
    <link:label id="lab_codi_SecondForbearanceAgreementMember_documentation_en-US" xlink:label="lab_codi_SecondForbearanceAgreementMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Second Forbearance Agreement</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_codi_SecondForbearanceAgreementMember" xlink:href="codi-20250331.xsd#codi_SecondForbearanceAgreementMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_codi_SecondForbearanceAgreementMember" xlink:to="lab_codi_SecondForbearanceAgreementMember" xlink:type="arc" order="1"/>
    <link:label id="lab_codi_PaymentsForRepurchaseSubsidiaryStock_97211fba-0d31-4e18-a3d1-1a8be1708bca_terseLabel_en-US" xlink:label="lab_codi_PaymentsForRepurchaseSubsidiaryStock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Payments for Repurchase Subsidiary Stock</link:label>
    <link:label id="lab_codi_PaymentsForRepurchaseSubsidiaryStock_label_en-US" xlink:label="lab_codi_PaymentsForRepurchaseSubsidiaryStock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Payments for Repurchase Subsidiary Stock</link:label>
    <link:label id="lab_codi_PaymentsForRepurchaseSubsidiaryStock_documentation_en-US" xlink:label="lab_codi_PaymentsForRepurchaseSubsidiaryStock" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Payments for Repurchase Subsidiary Stock</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_codi_PaymentsForRepurchaseSubsidiaryStock" xlink:href="codi-20250331.xsd#codi_PaymentsForRepurchaseSubsidiaryStock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_codi_PaymentsForRepurchaseSubsidiaryStock" xlink:to="lab_codi_PaymentsForRepurchaseSubsidiaryStock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_IncomeStatementBalanceSheetAndAdditionalDisclosuresByDisposalGroupsIncludingDiscontinuedOperationsAxis_376f6389-deda-4c5c-a094-63746032582b_terseLabel_en-US" xlink:label="lab_us-gaap_IncomeStatementBalanceSheetAndAdditionalDisclosuresByDisposalGroupsIncludingDiscontinuedOperationsAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Disposal Group Name [Axis]</link:label>
    <link:label id="lab_us-gaap_IncomeStatementBalanceSheetAndAdditionalDisclosuresByDisposalGroupsIncludingDiscontinuedOperationsAxis_label_en-US" xlink:label="lab_us-gaap_IncomeStatementBalanceSheetAndAdditionalDisclosuresByDisposalGroupsIncludingDiscontinuedOperationsAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Disposal Group Name [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncomeStatementBalanceSheetAndAdditionalDisclosuresByDisposalGroupsIncludingDiscontinuedOperationsAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_IncomeStatementBalanceSheetAndAdditionalDisclosuresByDisposalGroupsIncludingDiscontinuedOperationsAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_IncomeStatementBalanceSheetAndAdditionalDisclosuresByDisposalGroupsIncludingDiscontinuedOperationsAxis" xlink:to="lab_us-gaap_IncomeStatementBalanceSheetAndAdditionalDisclosuresByDisposalGroupsIncludingDiscontinuedOperationsAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_codi_SternoProductsMember_666b5ab5-a0ca-4b91-94f4-396661a637ab_terseLabel_en-US" xlink:label="lab_codi_SternoProductsMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Sterno Products [Member]</link:label>
    <link:label id="lab_codi_SternoProductsMember_label_en-US" xlink:label="lab_codi_SternoProductsMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Sterno Products [Member]</link:label>
    <link:label id="lab_codi_SternoProductsMember_documentation_en-US" xlink:label="lab_codi_SternoProductsMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Sterno Products [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_codi_SternoProductsMember" xlink:href="codi-20250331.xsd#codi_SternoProductsMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_codi_SternoProductsMember" xlink:to="lab_codi_SternoProductsMember" xlink:type="arc" order="1"/>
    <link:label id="lab_codi_A2022TermLoanMember_a3dda0ec-901d-4149-ad12-04e07b716026_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>
    <link:loc xlink:type="locator" xlink:label="loc_codi_A2022TermLoanMember" xlink:href="codi-20250331.xsd#codi_A2022TermLoanMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_codi_A2022TermLoanMember" xlink:to="lab_codi_A2022TermLoanMember" xlink:type="arc" order="1"/>
    <link:label id="lab_codi_DiamondFinancingLitigationMember_019b0da9-5b1e-7697-a7a8-b500c368dd3a_terseLabel_en-US" xlink:label="lab_codi_DiamondFinancingLitigationMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Diamond Financing Litigation</link:label>
    <link:label id="lab_codi_DiamondFinancingLitigationMember_label_en-US" xlink:label="lab_codi_DiamondFinancingLitigationMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Diamond Financing Litigation [Member]</link:label>
    <link:label id="lab_codi_DiamondFinancingLitigationMember_documentation_en-US" xlink:label="lab_codi_DiamondFinancingLitigationMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Diamond Financing Litigation</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_codi_DiamondFinancingLitigationMember" xlink:href="codi-20250331.xsd#codi_DiamondFinancingLitigationMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_codi_DiamondFinancingLitigationMember" xlink:to="lab_codi_DiamondFinancingLitigationMember" xlink:type="arc" order="1"/>
    <link:label id="lab_codi_PaymentstoNoncontrollingInterestsAllocationInterests_51416e52-0d6f-4a8f-91f1-24393eb39974_negatedTerseLabel_en-US" xlink:label="lab_codi_PaymentstoNoncontrollingInterestsAllocationInterests" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Payments to Noncontrolling Interests, Allocation Interests</link:label>
    <link:label id="lab_codi_PaymentstoNoncontrollingInterestsAllocationInterests_label_en-US" xlink:label="lab_codi_PaymentstoNoncontrollingInterestsAllocationInterests" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Payments to Noncontrolling Interests, Allocation Interests</link:label>
    <link:label id="lab_codi_PaymentstoNoncontrollingInterestsAllocationInterests_documentation_en-US" xlink:label="lab_codi_PaymentstoNoncontrollingInterestsAllocationInterests" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Payments to Noncontrolling Interests, Allocation Interests</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_codi_PaymentstoNoncontrollingInterestsAllocationInterests" xlink:href="codi-20250331.xsd#codi_PaymentstoNoncontrollingInterestsAllocationInterests"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_codi_PaymentstoNoncontrollingInterestsAllocationInterests" xlink:to="lab_codi_PaymentstoNoncontrollingInterestsAllocationInterests" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ScheduleOfFiniteLivedIntangibleAssetsTable_d226bc53-d101-4c69-bb9f-30286a55494c_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfFiniteLivedIntangibleAssetsTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Finite-Lived Intangible Assets [Table]</link:label>
    <link:label id="lab_us-gaap_ScheduleOfFiniteLivedIntangibleAssetsTable_label_en-US" xlink:label="lab_us-gaap_ScheduleOfFiniteLivedIntangibleAssetsTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Intangible Asset, Finite-Lived [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfFiniteLivedIntangibleAssetsTable" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ScheduleOfFiniteLivedIntangibleAssetsTable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ScheduleOfFiniteLivedIntangibleAssetsTable" xlink:to="lab_us-gaap_ScheduleOfFiniteLivedIntangibleAssetsTable" xlink:type="arc" order="1"/>
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    <link:label id="lab_us-gaap_OtherComprehensiveIncomeLossNetOfTaxPortionAttributableToParent_cb4b9e69-a117-4e5c-88a1-5131fbb13fc3_totalLabel_en-US" xlink:label="lab_us-gaap_OtherComprehensiveIncomeLossNetOfTaxPortionAttributableToParent" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Other Comprehensive Income (Loss), Net of Tax, Portion Attributable to Parent</link:label>
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    <link:label id="lab_us-gaap_LiabilitiesCurrentAbstract_6a9a8d58-b424-4d62-a334-e565c6bef2b5_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/2025/elts/us-gaap-2025.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_srt_StatementGeographicalAxis_086fede9-1b92-4450-b885-f8bd5c147a6a_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>
    <link:loc xlink:type="locator" xlink:label="loc_srt_StatementGeographicalAxis" xlink:href="https://xbrl.fasb.org/srt/2025/elts/srt-2025.xsd#srt_StatementGeographicalAxis"/>
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    <link:label id="lab_us-gaap_DebtInstrumentPeriodicPayment_d61d6d4a-3e81-4683-ae74-4b963022afd4_terseLabel_en-US" xlink:label="lab_us-gaap_DebtInstrumentPeriodicPayment" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Debt Instrument, Periodic Payment</link:label>
    <link:label id="lab_us-gaap_DebtInstrumentPeriodicPayment_label_en-US" xlink:label="lab_us-gaap_DebtInstrumentPeriodicPayment" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Instrument, Periodic Payment</link:label>
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    <link:label id="lab_codi_AtTheMarketEquityOfferingMember_629a572d-f577-413f-8888-cd06f8efae5a_terseLabel_en-US" xlink:label="lab_codi_AtTheMarketEquityOfferingMember" 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_AtTheMarketEquityOfferingMember_label_en-US" xlink:label="lab_codi_AtTheMarketEquityOfferingMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">At the market equity offering [Member]</link:label>
    <link:label id="lab_codi_AtTheMarketEquityOfferingMember_documentation_en-US" xlink:label="lab_codi_AtTheMarketEquityOfferingMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">At the market equity offering</link:label>
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    <link:label id="lab_codi_FifthForbearanceAgreementMember_019b23ad-ce23-79cc-bb05-a39520233d89_terseLabel_en-US" xlink:label="lab_codi_FifthForbearanceAgreementMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Fifth Forbearance Agreement</link:label>
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    <link:label id="lab_codi_FifthForbearanceAgreementMember_documentation_en-US" xlink:label="lab_codi_FifthForbearanceAgreementMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Fifth Forbearance Agreement</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_codi_FifthForbearanceAgreementMember" xlink:href="codi-20250331.xsd#codi_FifthForbearanceAgreementMember"/>
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    <link:label id="lab_us-gaap_FairValueInputsLevel1Member_8c15fe90-327b-4f94-a549-e2c6ce061112_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueInputsLevel1Member" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Level&#160;1</link:label>
    <link:label id="lab_us-gaap_FairValueInputsLevel1Member_label_en-US" xlink:label="lab_us-gaap_FairValueInputsLevel1Member" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fair Value, Inputs, Level 1 [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueInputsLevel1Member" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FairValueInputsLevel1Member"/>
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    <link:label id="lab_us-gaap_PreferredStockNoParValue_231fd1a1-b9ad-4ce8-a5c7-3eb3ce0f61b9_terseLabel_en-US" xlink:label="lab_us-gaap_PreferredStockNoParValue" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Preferred Stock, No Par Value</link:label>
    <link:label id="lab_us-gaap_PreferredStockNoParValue_label_en-US" xlink:label="lab_us-gaap_PreferredStockNoParValue" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Preferred Stock, No Par Value</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PreferredStockNoParValue" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_PreferredStockNoParValue"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PreferredStockNoParValue" xlink:to="lab_us-gaap_PreferredStockNoParValue" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_BusinessAcquisitionsProFormaRevenue_99be2598-815a-4115-863e-e46e13ac210c_terseLabel_en-US" xlink:label="lab_us-gaap_BusinessAcquisitionsProFormaRevenue" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Business Combination, Pro Forma Information, Pro Forma Revenue</link:label>
    <link:label id="lab_us-gaap_BusinessAcquisitionsProFormaRevenue_label_en-US" xlink:label="lab_us-gaap_BusinessAcquisitionsProFormaRevenue" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Business Combination, Pro Forma Information, Pro Forma Revenue</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_BusinessAcquisitionsProFormaRevenue" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_BusinessAcquisitionsProFormaRevenue"/>
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    <link:label id="lab_us-gaap_PreferredStockRedemptionPricePerShare_a3f18b83-bf10-46c7-8d91-8dfc7713bca7_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/2025/elts/us-gaap-2025.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_ScheduleOfRelatedPartyTransactionsByRelatedPartyTable_e7a0735b-aa0b-4d16-8889-afd0f120be5f_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">Schedule of Related Party Transactions, by Related Party [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/2025/elts/us-gaap-2025.xsd#us-gaap_ScheduleOfRelatedPartyTransactionsByRelatedPartyTable"/>
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    <link:label id="lab_srt_AsiaPacificMember_c3fdfb34-b9f1-48a5-badd-f0c11ca06587_terseLabel_en-US" xlink:label="lab_srt_AsiaPacificMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Asia Pacific [Member]</link:label>
    <link:label id="lab_srt_AsiaPacificMember_label_en-US" xlink:label="lab_srt_AsiaPacificMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Asia Pacific [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_srt_AsiaPacificMember" xlink:href="https://xbrl.fasb.org/srt/2025/elts/srt-2025.xsd#srt_AsiaPacificMember"/>
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    <link:label id="lab_us-gaap_EarningsPerShareDiluted_00684443-cb4a-4d90-8a97-504c85246fe2_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_codi_VelocityOutdoorOwnershipMember_62b5b9a6-1688-42dd-8487-88756fd292fd_terseLabel_en-US" xlink:label="lab_codi_VelocityOutdoorOwnershipMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Velocity Outdoor</link:label>
    <link:label id="lab_codi_VelocityOutdoorOwnershipMember_label_en-US" xlink:label="lab_codi_VelocityOutdoorOwnershipMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Velocity Outdoor Ownership [Member]</link:label>
    <link:label id="lab_codi_VelocityOutdoorOwnershipMember_documentation_en-US" xlink:label="lab_codi_VelocityOutdoorOwnershipMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Velocity Outdoor Ownership [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_codi_VelocityOutdoorOwnershipMember" xlink:href="codi-20250331.xsd#codi_VelocityOutdoorOwnershipMember"/>
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    <link:label id="lab_us-gaap_AccountsReceivableNetCurrent_b2bb7949-d710-4d80-a602-6bea1656fd9f_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_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/2025/elts/us-gaap-2025.xsd#us-gaap_AccountsReceivableNetCurrent"/>
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    <link:label id="lab_dei_Security12bTitle_fe90fe2d-00df-45ac-b7bc-06e1e7eeea29_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>
    <link:label id="lab_dei_Security12bTitle_label_en-US" xlink:label="lab_dei_Security12bTitle" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Title of 12(b) Security</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_Security12bTitle" xlink:href="https://xbrl.sec.gov/dei/2025/dei-2025.xsd#dei_Security12bTitle"/>
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    <link:label id="lab_us-gaap_IncomeStatementBalanceSheetAndAdditionalDisclosuresByDisposalGroupsIncludingDiscontinuedOperationsTable_09b4bc47-f901-4612-af44-4cf9074db00c_terseLabel_en-US" xlink:label="lab_us-gaap_IncomeStatementBalanceSheetAndAdditionalDisclosuresByDisposalGroupsIncludingDiscontinuedOperationsTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Disposal Groups, Including Discontinued Operations [Table]</link:label>
    <link:label id="lab_us-gaap_IncomeStatementBalanceSheetAndAdditionalDisclosuresByDisposalGroupsIncludingDiscontinuedOperationsTable_label_en-US" xlink:label="lab_us-gaap_IncomeStatementBalanceSheetAndAdditionalDisclosuresByDisposalGroupsIncludingDiscontinuedOperationsTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Disposal Groups, Including Discontinued Operations [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncomeStatementBalanceSheetAndAdditionalDisclosuresByDisposalGroupsIncludingDiscontinuedOperationsTable" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_IncomeStatementBalanceSheetAndAdditionalDisclosuresByDisposalGroupsIncludingDiscontinuedOperationsTable"/>
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    <link:label id="lab_us-gaap_DefinedBenefitPlanExpectedFutureEmployerContributionsRemainderOfFiscalYear_90022f21-08bc-4a35-a174-5e6cb9495f85_terseLabel_en-US" xlink:label="lab_us-gaap_DefinedBenefitPlanExpectedFutureEmployerContributionsRemainderOfFiscalYear" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Expected contribution to the Foreign Plan</link:label>
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    <link:label id="lab_codi_AtTheMarketOfferingCosts_a9f65ee2-c890-4859-8e44-d628c8b0b0ad_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-20250331.xsd#codi_AtTheMarketOfferingCosts"/>
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    <link:label id="lab_codi_OperatingAndFinancingLeaseLiabilityToBePaidAfterYearFive_c1f89e68-72c1-4e7a-8557-68a10cb465a1_terseLabel_en-US" xlink:label="lab_codi_OperatingAndFinancingLeaseLiabilityToBePaidAfterYearFive" 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>
    <link:label id="lab_codi_OperatingAndFinancingLeaseLiabilityToBePaidAfterYearFive_label_en-US" xlink:label="lab_codi_OperatingAndFinancingLeaseLiabilityToBePaidAfterYearFive" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Operating and Financing Lease, Liability, to be Paid, After Year Five</link:label>
    <link:label id="lab_codi_OperatingAndFinancingLeaseLiabilityToBePaidAfterYearFive_documentation_en-US" xlink:label="lab_codi_OperatingAndFinancingLeaseLiabilityToBePaidAfterYearFive" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Operating and Financing Lease, Liability, to be Paid, After Year Five</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_codi_OperatingAndFinancingLeaseLiabilityToBePaidAfterYearFive" xlink:href="codi-20250331.xsd#codi_OperatingAndFinancingLeaseLiabilityToBePaidAfterYearFive"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_codi_OperatingAndFinancingLeaseLiabilityToBePaidAfterYearFive" xlink:to="lab_codi_OperatingAndFinancingLeaseLiabilityToBePaidAfterYearFive" xlink:type="arc" order="1"/>
    <link:label id="lab_srt_ConsolidationItemsDomain_3a3cfe23-cd75-4bc7-bca3-f8cbcc673304_terseLabel_en-US" xlink:label="lab_srt_ConsolidationItemsDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Consolidation Items [Domain]</link:label>
    <link:label id="lab_srt_ConsolidationItemsDomain_label_en-US" xlink:label="lab_srt_ConsolidationItemsDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Consolidation Items [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_srt_ConsolidationItemsDomain" xlink:href="https://xbrl.fasb.org/srt/2025/elts/srt-2025.xsd#srt_ConsolidationItemsDomain"/>
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    <link:label id="lab_us-gaap_MinorityInterestOwnershipPercentageByParent_5c00fd5f-48fe-4fff-9705-f0c3df73a074_terseLabel_en-US" xlink:label="lab_us-gaap_MinorityInterestOwnershipPercentageByParent" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Noncontrolling Interest, Ownership Percentage by Parent</link:label>
    <link:label id="lab_us-gaap_MinorityInterestOwnershipPercentageByParent_label_en-US" xlink:label="lab_us-gaap_MinorityInterestOwnershipPercentageByParent" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Subsidiary, Ownership Percentage, Parent</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_MinorityInterestOwnershipPercentageByParent" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_MinorityInterestOwnershipPercentageByParent"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_MinorityInterestOwnershipPercentageByParent" xlink:to="lab_us-gaap_MinorityInterestOwnershipPercentageByParent" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_IncomeLossFromDiscontinuedOperationsNetOfTax_0fb88e5b-f438-4f95-89c5-7a5a7a1cbe78_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 Tax, Including Portion Attributable to Noncontrolling Interest</link:label>
    <link:label id="lab_us-gaap_IncomeLossFromDiscontinuedOperationsNetOfTax_95d1d9ca-ed32-43c4-9bd0-35e3f695bc6c_totalLabel_en-US" xlink:label="lab_us-gaap_IncomeLossFromDiscontinuedOperationsNetOfTax" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Income from discontinued operations</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>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncomeLossFromDiscontinuedOperationsNetOfTax" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_IncomeLossFromDiscontinuedOperationsNetOfTax"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_IncomeLossFromDiscontinuedOperationsNetOfTax" xlink:to="lab_us-gaap_IncomeLossFromDiscontinuedOperationsNetOfTax" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_GrossProfit_32545189-bf1c-41d0-9d1b-93533468f16c_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_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/2025/elts/us-gaap-2025.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_NoncontrollingInterestAbstract_11c7af4f-789c-42e3-92b9-6c45f06a83c7_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/2025/elts/us-gaap-2025.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_LesseeOperatingLeaseLiabilityUndiscountedExcessAmount_1322c390-fc97-4e3b-b806-23aec3203c11_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>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LesseeOperatingLeaseLiabilityUndiscountedExcessAmount" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_LesseeOperatingLeaseLiabilityUndiscountedExcessAmount"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LesseeOperatingLeaseLiabilityUndiscountedExcessAmount" xlink:to="lab_us-gaap_LesseeOperatingLeaseLiabilityUndiscountedExcessAmount" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FinanceLeaseLiabilityPaymentsDueAfterYearFive_7e0a195b-b1ab-4ca4-882a-c7f9e4ea246d_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>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FinanceLeaseLiabilityPaymentsDueAfterYearFive" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FinanceLeaseLiabilityPaymentsDueAfterYearFive"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FinanceLeaseLiabilityPaymentsDueAfterYearFive" xlink:to="lab_us-gaap_FinanceLeaseLiabilityPaymentsDueAfterYearFive" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseYearTwo_d1cc21bc-844e-4100-ac0e-feef45be1283_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">2023</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/2025/elts/us-gaap-2025.xsd#us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseYearTwo"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseYearTwo" xlink:to="lab_us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseYearTwo" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ScheduleOfInventoryCurrentTableTextBlock_1e3a76ae-ecf4-4637-a29b-66d2dc3295a2_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfInventoryCurrentTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Summary of Inventory</link:label>
    <link:label id="lab_us-gaap_ScheduleOfInventoryCurrentTableTextBlock_label_en-US" xlink:label="lab_us-gaap_ScheduleOfInventoryCurrentTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Schedule of Inventory, Current [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfInventoryCurrentTableTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ScheduleOfInventoryCurrentTableTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ScheduleOfInventoryCurrentTableTextBlock" xlink:to="lab_us-gaap_ScheduleOfInventoryCurrentTableTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DefinedBenefitPlanServiceCost_e1871360-8058-487b-9d04-6ab2206438f2_terseLabel_en-US" xlink:label="lab_us-gaap_DefinedBenefitPlanServiceCost" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Service cost</link:label>
    <link:label id="lab_us-gaap_DefinedBenefitPlanServiceCost_label_en-US" xlink:label="lab_us-gaap_DefinedBenefitPlanServiceCost" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Defined Benefit Plan, Service Cost</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DefinedBenefitPlanServiceCost" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DefinedBenefitPlanServiceCost"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DefinedBenefitPlanServiceCost" xlink:to="lab_us-gaap_DefinedBenefitPlanServiceCost" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DebtInstrumentCarryingAmount_9a5f8165-44eb-4078-9dce-a6602ca34425_terseLabel_en-US" xlink:label="lab_us-gaap_DebtInstrumentCarryingAmount" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Long-term Debt, Gross</link:label>
    <link:label id="lab_us-gaap_DebtInstrumentCarryingAmount_label_en-US" xlink:label="lab_us-gaap_DebtInstrumentCarryingAmount" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Long-Term Debt, Gross</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtInstrumentCarryingAmount" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DebtInstrumentCarryingAmount"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DebtInstrumentCarryingAmount" xlink:to="lab_us-gaap_DebtInstrumentCarryingAmount" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FairValueMeasurementFrequencyDomain_0ffd292c-9026-4309-8a13-5a1b00ef54b6_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueMeasurementFrequencyDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Measurement Frequency [Domain]</link:label>
    <link:label id="lab_us-gaap_FairValueMeasurementFrequencyDomain_label_en-US" xlink:label="lab_us-gaap_FairValueMeasurementFrequencyDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Measurement Frequency [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueMeasurementFrequencyDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FairValueMeasurementFrequencyDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FairValueMeasurementFrequencyDomain" xlink:to="lab_us-gaap_FairValueMeasurementFrequencyDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_codi_OperatingAndFinanceLeaseLiability_63d50e5e-09fc-4be5-a80e-a40abed394e2_terseLabel_en-US" xlink:label="lab_codi_OperatingAndFinanceLeaseLiability" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Operating and Finance Lease, Liability</link:label>
    <link:label id="lab_codi_OperatingAndFinanceLeaseLiability_label_en-US" xlink:label="lab_codi_OperatingAndFinanceLeaseLiability" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Operating and Finance Lease, Liability</link:label>
    <link:label id="lab_codi_OperatingAndFinanceLeaseLiability_documentation_en-US" xlink:label="lab_codi_OperatingAndFinanceLeaseLiability" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Operating and Finance Lease, Liability</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_codi_OperatingAndFinanceLeaseLiability" xlink:href="codi-20250331.xsd#codi_OperatingAndFinanceLeaseLiability"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_codi_OperatingAndFinanceLeaseLiability" xlink:to="lab_codi_OperatingAndFinanceLeaseLiability" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDue_a154fd7b-d4a5-48b9-b059-1827d174069c_totalLabel_en-US" xlink:label="lab_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDue" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Total undiscounted lease payments</link:label>
    <link:label id="lab_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDue_label_en-US" xlink:label="lab_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDue" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Lessee, Operating Lease, Liability, to be Paid</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDue" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_LesseeOperatingLeaseLiabilityPaymentsDue"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDue" xlink:to="lab_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDue" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisAbstract_3ee905b1-41dd-4101-a0d8-d279b8cb04a6_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Liabilities:</link:label>
    <link:label id="lab_us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisAbstract_label_en-US" xlink:label="lab_us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisAbstract" 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 [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisAbstract" xlink:to="lab_us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_codi_BusinessCombinationProvisionalInformationInitialAccountingIncompleteAdjustmentDeferredTaxLiabilities_e5f82549-392d-4888-bdfe-60d0eb2de773_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>
    <link:label id="lab_codi_BusinessCombinationProvisionalInformationInitialAccountingIncompleteAdjustmentDeferredTaxLiabilities_label_en-US" xlink:label="lab_codi_BusinessCombinationProvisionalInformationInitialAccountingIncompleteAdjustmentDeferredTaxLiabilities" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Business Combination, Provisional Information, Initial Accounting Incomplete, Adjustment, Deferred Tax Liabilities</link:label>
    <link:label id="lab_codi_BusinessCombinationProvisionalInformationInitialAccountingIncompleteAdjustmentDeferredTaxLiabilities_documentation_en-US" xlink:label="lab_codi_BusinessCombinationProvisionalInformationInitialAccountingIncompleteAdjustmentDeferredTaxLiabilities" xlink:role="http://www.xbrl.org/2003/role/documentation" 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:label id="lab_codi_OperatingAndFinanceLeaseLiabilityToBePaidYearOne_190cc4fd-5405-4a69-817d-b92eb1be351d_terseLabel_en-US" xlink:label="lab_codi_OperatingAndFinanceLeaseLiabilityToBePaidYearOne" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Operating and Finance Lease, Liability, to be Paid, Year One</link:label>
    <link:label id="lab_codi_OperatingAndFinanceLeaseLiabilityToBePaidYearOne_label_en-US" xlink:label="lab_codi_OperatingAndFinanceLeaseLiabilityToBePaidYearOne" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Operating and Finance Lease, Liability, to be Paid, Year One</link:label>
    <link:label id="lab_codi_OperatingAndFinanceLeaseLiabilityToBePaidYearOne_documentation_en-US" xlink:label="lab_codi_OperatingAndFinanceLeaseLiabilityToBePaidYearOne" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Operating and Finance Lease, Liability, to be Paid, Year One</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_codi_OperatingAndFinanceLeaseLiabilityToBePaidYearOne" xlink:href="codi-20250331.xsd#codi_OperatingAndFinanceLeaseLiabilityToBePaidYearOne"/>
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    <link:label id="lab_codi_BusinessCombinationIntegrationServicesPayable_65ec1bf5-f6a7-4afb-b002-473d1e64a0e4_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 payable</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>
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    <link:label id="lab_us-gaap_TradeNamesMember_8f22ec22-4059-4e4e-b04a-a9b80debb44c_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>
    <link:label id="lab_us-gaap_TradeNamesMember_8f9236bd-c95d-413b-8fd6-a81678eff520_verboseLabel_en-US" xlink:label="lab_us-gaap_TradeNamesMember" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Trade Names [Member]</link:label>
    <link:label id="lab_us-gaap_TradeNamesMember_label_en-US" xlink:label="lab_us-gaap_TradeNamesMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Trade Names [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_TradeNamesMember" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_TradeNamesMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_TradeNamesMember" xlink:to="lab_us-gaap_TradeNamesMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_NetIncomeLoss_8a6b6cb7-d4fa-4bb1-b26c-b8f09157da27_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 loss attributable to Holdings</link:label>
    <link:label id="lab_us-gaap_NetIncomeLoss_8aa05fca-2228-4018-a408-2f2c5e45aa9c_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 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/2025/elts/us-gaap-2025.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_us-gaap_SubsequentEventTable_ef6fdec0-badf-4441-86ac-9b0074224680_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/2025/elts/us-gaap-2025.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"/>
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    <link:label id="lab_us-gaap_ScheduleOfEffectiveIncomeTaxRateReconciliationTableTextBlock_label_en-US" xlink:label="lab_us-gaap_ScheduleOfEffectiveIncomeTaxRateReconciliationTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Schedule of Effective Income Tax Rate Reconciliation [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfEffectiveIncomeTaxRateReconciliationTableTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ScheduleOfEffectiveIncomeTaxRateReconciliationTableTextBlock"/>
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    <link:label id="lab_us-gaap_StockholdersEquityIncludingPortionAttributableToNoncontrollingInterestAbstract_9b1075ab-ea36-497e-9ff9-2c7fb6bc7b53_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:label id="lab_us-gaap_EffectiveIncomeTaxRateReconciliationOtherAdjustments_350b06cf-28df-4192-bfc7-e21c339b8297_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/2025/elts/us-gaap-2025.xsd#us-gaap_EffectiveIncomeTaxRateReconciliationOtherAdjustments"/>
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    <link:label id="lab_codi_OperatingAndFinancingLeaseLiabilityToBePaidYearTwo_8a0d122e-a152-4d09-b30d-bc550a44c36e_terseLabel_en-US" xlink:label="lab_codi_OperatingAndFinancingLeaseLiabilityToBePaidYearTwo" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">2027Lessee Operating and Financing Lease, Liability, to be Paid, Year Two</link:label>
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    <link:label id="lab_codi_OperatingAndFinancingLeaseLiabilityToBePaidYearTwo_documentation_en-US" xlink:label="lab_codi_OperatingAndFinancingLeaseLiabilityToBePaidYearTwo" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Operating and Financing Lease, Liability, to be Paid, Year Two</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_codi_OperatingAndFinancingLeaseLiabilityToBePaidYearTwo" xlink:href="codi-20250331.xsd#codi_OperatingAndFinancingLeaseLiabilityToBePaidYearTwo"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_codi_OperatingAndFinancingLeaseLiabilityToBePaidYearTwo" xlink:to="lab_codi_OperatingAndFinancingLeaseLiabilityToBePaidYearTwo" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_PropertyPlantAndEquipmentNet_ca1c4a30-c6b9-40a1-bc48-c2f4ddb2ee73_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_9e09c329-ef13-4524-ba6a-4b4c774c80c0_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>
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    <link:label id="lab_codi_NetIncomeLossAvailabletoTrustStockNetofDistributions_96b4dec9-c427-49d0-9be3-623d00f2e840_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>
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    <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-20250331.xsd#codi_NetIncomeLossAvailabletoTrustStockNetofDistributions"/>
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    <link:label id="lab_codi_PercentageRepresenationOfTotalCreditExposure_019b12c6-270c-7b42-9dda-2dd426641b62_terseLabel_en-US" xlink:label="lab_codi_PercentageRepresenationOfTotalCreditExposure" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Percentage represenation of total credit exposure</link:label>
    <link:label id="lab_codi_PercentageRepresenationOfTotalCreditExposure_label_en-US" xlink:label="lab_codi_PercentageRepresenationOfTotalCreditExposure" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Percentage represenation of total credit exposure</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_codi_PercentageRepresenationOfTotalCreditExposure" xlink:href="codi-20250331.xsd#codi_PercentageRepresenationOfTotalCreditExposure"/>
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    <link:label id="lab_us-gaap_SegmentReportingInformationLineItems_32752bd5-e5ba-402e-bd72-78a860eee20d_terseLabel_en-US" xlink:label="lab_us-gaap_SegmentReportingInformationLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Segment Reporting Information [Line Items]</link:label>
    <link:label id="lab_us-gaap_SegmentReportingInformationLineItems_label_en-US" xlink:label="lab_us-gaap_SegmentReportingInformationLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Segment Reporting Information [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SegmentReportingInformationLineItems" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_SegmentReportingInformationLineItems"/>
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    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PreferredStockSharesAuthorized" xlink:to="lab_us-gaap_PreferredStockSharesAuthorized" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_BaseRateMember_3f2d8df7-2a00-44df-ae54-d002e5b24ec0_terseLabel_en-US" xlink:label="lab_us-gaap_BaseRateMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Base Rate</link:label>
    <link:label id="lab_us-gaap_BaseRateMember_label_en-US" xlink:label="lab_us-gaap_BaseRateMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Base Rate [Member]</link:label>
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    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_BaseRateMember" xlink:to="lab_us-gaap_BaseRateMember" xlink:type="arc" order="1"/>
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    <link:label id="lab_us-gaap_PreferredClassAMember_d5c15002-6e3c-4bb1-9721-ba9440efb73d_terseLabel_en-US" xlink:label="lab_us-gaap_PreferredClassAMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Preferred Class A [Member]</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PreferredClassAMember" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_PreferredClassAMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PreferredClassAMember" xlink:to="lab_us-gaap_PreferredClassAMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_SeriesAPreferredStockMember_5ec4aaa6-3525-4f75-8010-b4d2ad6d908b_terseLabel_en-US" xlink:label="lab_us-gaap_SeriesAPreferredStockMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Series A Preferred Stock</link:label>
    <link:label id="lab_us-gaap_SeriesAPreferredStockMember_label_en-US" xlink:label="lab_us-gaap_SeriesAPreferredStockMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Series A Preferred Stock [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SeriesAPreferredStockMember" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_SeriesAPreferredStockMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_SeriesAPreferredStockMember" xlink:to="lab_us-gaap_SeriesAPreferredStockMember" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_EntityCurrentReportingStatus_fe3ea687-1fef-479b-8c42-f782af447ae0_terseLabel_en-US" xlink:label="lab_dei_EntityCurrentReportingStatus" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Entity Current Reporting Status</link:label>
    <link:label id="lab_dei_EntityCurrentReportingStatus_label_en-US" xlink:label="lab_dei_EntityCurrentReportingStatus" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Entity Current Reporting Status</link:label>
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    <link:label id="lab_us-gaap_CustomerRelationshipsMember_0b74272e-264e-43fb-aa8b-1b22f3254c48_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_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/2025/elts/us-gaap-2025.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_OperatingIncomeLoss_d02e611f-0c5a-4163-aec9-8eab954067ec_totalLabel_en-US" xlink:label="lab_us-gaap_OperatingIncomeLoss" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Operating income (loss)</link:label>
    <link:label id="lab_us-gaap_OperatingIncomeLoss_99c01f54-d479-49e6-a952-8c0863677355_terseLabel_en-US" xlink:label="lab_us-gaap_OperatingIncomeLoss" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Operating Income (Loss)</link:label>
    <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>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OperatingIncomeLoss" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_OperatingIncomeLoss"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OperatingIncomeLoss" xlink:to="lab_us-gaap_OperatingIncomeLoss" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LineOfCreditMember_c3f14426-aa92-40ce-9772-8b89bbf81b88_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/2025/elts/us-gaap-2025.xsd#us-gaap_LineOfCreditMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LineOfCreditMember" xlink:to="lab_us-gaap_LineOfCreditMember" xlink:type="arc" order="1"/>
    <link:label id="lab_codi_PercentageOwnershipFullyDilutedMember_389667cf-7a54-479e-a56d-72fd7b9bb44f_terseLabel_en-US" xlink:label="lab_codi_PercentageOwnershipFullyDilutedMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">% Ownership 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-20250331.xsd#codi_PercentageOwnershipFullyDilutedMember"/>
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    <link:label id="lab_us-gaap_RetainedEarningsAccumulatedDeficit_798c3ea6-dd04-477f-9ecb-036597745301_terseLabel_en-US" xlink:label="lab_us-gaap_RetainedEarningsAccumulatedDeficit" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Accumulated deficit</link:label>
    <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>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_RetainedEarningsAccumulatedDeficit" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_RetainedEarningsAccumulatedDeficit"/>
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    <link:label id="lab_us-gaap_CorporateMember_019b14ac-52cc-7a7f-b7a6-26991045281b_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 Segment</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>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CorporateMember" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_CorporateMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CorporateMember" xlink:to="lab_us-gaap_CorporateMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_StatementOfFinancialPositionAbstract_42f02f13-57cc-4608-ba81-1a2a51a5ac31_terseLabel_en-US" xlink:label="lab_us-gaap_StatementOfFinancialPositionAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Statement of Financial Position [Abstract]</link:label>
    <link:label id="lab_us-gaap_StatementOfFinancialPositionAbstract_label_en-US" xlink:label="lab_us-gaap_StatementOfFinancialPositionAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Statement of Financial Position [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_StatementOfFinancialPositionAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_StatementOfFinancialPositionAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_StatementOfFinancialPositionAbstract" xlink:to="lab_us-gaap_StatementOfFinancialPositionAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_codi_PropertyPlantAndEquipmentAndInventoryTextBlock_b727355c-e306-40ba-889c-1afa5ecfb830_terseLabel_en-US" xlink:label="lab_codi_PropertyPlantAndEquipmentAndInventoryTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Property, Plant and Equipment and Inventory</link:label>
    <link:label id="lab_codi_PropertyPlantAndEquipmentAndInventoryTextBlock_label_en-US" xlink:label="lab_codi_PropertyPlantAndEquipmentAndInventoryTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Property Plant And Equipment And Inventory [Text Block]</link:label>
    <link:label id="lab_codi_PropertyPlantAndEquipmentAndInventoryTextBlock_documentation_en-US" xlink:label="lab_codi_PropertyPlantAndEquipmentAndInventoryTextBlock" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Property, plant and equipment and inventory.</link:label>
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    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_codi_PropertyPlantAndEquipmentAndInventoryTextBlock" xlink:to="lab_codi_PropertyPlantAndEquipmentAndInventoryTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_EffectiveIncomeTaxRateReconciliationNondeductibleExpenseShareBasedCompensationCost_5d494a04-f164-41c0-8086-38845be34d39_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, Amount</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>
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    <link:label id="lab_us-gaap_EffectiveIncomeTaxRateReconciliationStateAndLocalIncomeTaxes_6c28ca7c-d2e8-4e6f-a301-630c975e1934_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>
    <link:label id="lab_us-gaap_EffectiveIncomeTaxRateReconciliationStateAndLocalIncomeTaxes_label_en-US" xlink:label="lab_us-gaap_EffectiveIncomeTaxRateReconciliationStateAndLocalIncomeTaxes" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Effective Income Tax Rate Reconciliation, State and Local Income Taxes, Percent</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_EffectiveIncomeTaxRateReconciliationStateAndLocalIncomeTaxes" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_EffectiveIncomeTaxRateReconciliationStateAndLocalIncomeTaxes"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_EffectiveIncomeTaxRateReconciliationStateAndLocalIncomeTaxes" xlink:to="lab_us-gaap_EffectiveIncomeTaxRateReconciliationStateAndLocalIncomeTaxes" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FinanceLeaseLiabilityCurrent_019b23d3-0408-7805-8771-6907987a7f32_terseLabel_en-US" xlink:label="lab_us-gaap_FinanceLeaseLiabilityCurrent" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Finance Lease, Liability, Current</link:label>
    <link:label id="lab_us-gaap_FinanceLeaseLiabilityCurrent_label_en-US" xlink:label="lab_us-gaap_FinanceLeaseLiabilityCurrent" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Finance Lease, Liability, Current</link:label>
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    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FinanceLeaseLiabilityCurrent" xlink:to="lab_us-gaap_FinanceLeaseLiabilityCurrent" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_InventoryValuationReserves_1c4c0227-c3db-4f8b-ae03-423dc9827acd_negatedLabel_en-US" xlink:label="lab_us-gaap_InventoryValuationReserves" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:type="resource" xml:lang="en-US">Less: obsolescence reserve</link:label>
    <link:label id="lab_us-gaap_InventoryValuationReserves_label_en-US" xlink:label="lab_us-gaap_InventoryValuationReserves" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Inventory Valuation Reserves</link:label>
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    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_InventoryValuationReserves" xlink:to="lab_us-gaap_InventoryValuationReserves" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_InterestExpense_536303e3-4396-4d97-97e8-d993afa8c276_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, 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/2025/elts/us-gaap-2025.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_dei_CurrentFiscalYearEndDate_a94565ec-b978-4454-9621-84b2c1b6c65b_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>
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    <link:loc xlink:type="locator" xlink:label="loc_dei_CurrentFiscalYearEndDate" xlink:href="https://xbrl.sec.gov/dei/2025/dei-2025.xsd#dei_CurrentFiscalYearEndDate"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_CurrentFiscalYearEndDate" xlink:to="lab_dei_CurrentFiscalYearEndDate" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_StatementClassOfStockAxis_b6df90bd-b95c-448b-b7b7-eccbf46b327a_terseLabel_en-US" xlink:label="lab_us-gaap_StatementClassOfStockAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Class of Stock [Axis]</link:label>
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    <link:label id="lab_us-gaap_SubsequentEventTypeDomain_5282f071-f619-4785-b3bd-aa8e2cbc5a1c_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/2025/elts/us-gaap-2025.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_us-gaap_FiniteLivedIntangibleAssetsMajorClassNameDomain_4770d7d7-ce0a-4467-9fe0-66acee14c242_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>
    <link:label id="lab_us-gaap_FiniteLivedIntangibleAssetsMajorClassNameDomain_label_en-US" xlink:label="lab_us-gaap_FiniteLivedIntangibleAssetsMajorClassNameDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Finite-Lived Intangible Assets, Major Class Name [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FiniteLivedIntangibleAssetsMajorClassNameDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FiniteLivedIntangibleAssetsMajorClassNameDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FiniteLivedIntangibleAssetsMajorClassNameDomain" xlink:to="lab_us-gaap_FiniteLivedIntangibleAssetsMajorClassNameDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OtherNonoperatingIncomeExpense_15a72045-50c0-402a-8553-d75eb2a0931e_terseLabel_en-US" xlink:label="lab_us-gaap_OtherNonoperatingIncomeExpense" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Other income (expense), net</link:label>
    <link:label id="lab_us-gaap_OtherNonoperatingIncomeExpense_4121e8c9-6b56-4d93-8c2b-57135988a4ec_verboseLabel_en-US" xlink:label="lab_us-gaap_OtherNonoperatingIncomeExpense" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Other Nonoperating Income (Expense)</link:label>
    <link:label id="lab_us-gaap_OtherNonoperatingIncomeExpense_label_en-US" xlink:label="lab_us-gaap_OtherNonoperatingIncomeExpense" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Other Nonoperating Income (Expense)</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OtherNonoperatingIncomeExpense" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_OtherNonoperatingIncomeExpense"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OtherNonoperatingIncomeExpense" xlink:to="lab_us-gaap_OtherNonoperatingIncomeExpense" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_StatementTable_336e7c3b-ce92-4220-a0f4-905e7a984960_terseLabel_en-US" xlink:label="lab_us-gaap_StatementTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Statement [Table]</link:label>
    <link:label id="lab_us-gaap_StatementTable_label_en-US" xlink:label="lab_us-gaap_StatementTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Statement [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_StatementTable" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_StatementTable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_StatementTable" xlink:to="lab_us-gaap_StatementTable" xlink:type="arc" order="1"/>
    <link:label id="lab_codi_SwingLineLoanMember_f3984bf4-44b7-4c55-b769-d308046b3687_terseLabel_en-US" xlink:label="lab_codi_SwingLineLoanMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Swing line loan</link:label>
    <link:label id="lab_codi_SwingLineLoanMember_label_en-US" xlink:label="lab_codi_SwingLineLoanMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Swing line loan [Member]</link:label>
    <link:label id="lab_codi_SwingLineLoanMember_documentation_en-US" xlink:label="lab_codi_SwingLineLoanMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Swing line loan</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_codi_SwingLineLoanMember" xlink:href="codi-20250331.xsd#codi_SwingLineLoanMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_codi_SwingLineLoanMember" xlink:to="lab_codi_SwingLineLoanMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_EffectOfExchangeRateOnCashCashEquivalentsRestrictedCashAndRestrictedCashEquivalentsIncludingDisposalGroupAndDiscontinuedOperations_b3c71d61-9ef8-4e09-9c0d-364be3459f7f_terseLabel_en-US" xlink:label="lab_us-gaap_EffectOfExchangeRateOnCashCashEquivalentsRestrictedCashAndRestrictedCashEquivalentsIncludingDisposalGroupAndDiscontinuedOperations" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Foreign currency impact on cash</link:label>
    <link:label id="lab_us-gaap_EffectOfExchangeRateOnCashCashEquivalentsRestrictedCashAndRestrictedCashEquivalentsIncludingDisposalGroupAndDiscontinuedOperations_label_en-US" xlink:label="lab_us-gaap_EffectOfExchangeRateOnCashCashEquivalentsRestrictedCashAndRestrictedCashEquivalentsIncludingDisposalGroupAndDiscontinuedOperations" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Effect of Exchange Rate on Cash, Cash Equivalent, Restricted Cash, and Restricted Cash Equivalent, Including Discontinued Operation</link:label>
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    <link:label id="lab_us-gaap_AdjustmentsToReconcileNetIncomeLossToCashProvidedByUsedInOperatingActivitiesAbstract_a3ec9eaa-1ea5-4dfa-a03c-b5321553070a_terseLabel_en-US" xlink:label="lab_us-gaap_AdjustmentsToReconcileNetIncomeLossToCashProvidedByUsedInOperatingActivitiesAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Adjustments to reconcile net loss to net cash provided by (used in) operating activities:</link:label>
    <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">Adjustment to Reconcile Net Income to Cash Provided by (Used in) Operating Activity [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AdjustmentsToReconcileNetIncomeLossToCashProvidedByUsedInOperatingActivitiesAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_AdjustmentsToReconcileNetIncomeLossToCashProvidedByUsedInOperatingActivitiesAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AdjustmentsToReconcileNetIncomeLossToCashProvidedByUsedInOperatingActivitiesAbstract" xlink:to="lab_us-gaap_AdjustmentsToReconcileNetIncomeLossToCashProvidedByUsedInOperatingActivitiesAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_codi_LineOfCreditFacilityRevolvingCreditExposure_019b12ca-a7e8-793b-b862-e854c9b17b90_terseLabel_en-US" xlink:label="lab_codi_LineOfCreditFacilityRevolvingCreditExposure" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Line of Credit Facility, revolving credit exposure</link:label>
    <link:label id="lab_codi_LineOfCreditFacilityRevolvingCreditExposure_label_en-US" xlink:label="lab_codi_LineOfCreditFacilityRevolvingCreditExposure" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Line of Credit Facility, revolving credit exposure</link:label>
    <link:label id="lab_codi_LineOfCreditFacilityRevolvingCreditExposure_documentation_en-US" xlink:label="lab_codi_LineOfCreditFacilityRevolvingCreditExposure" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Line of Credit Facility, revolving credit exposure</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_codi_LineOfCreditFacilityRevolvingCreditExposure" xlink:href="codi-20250331.xsd#codi_LineOfCreditFacilityRevolvingCreditExposure"/>
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    <link:label id="lab_us-gaap_NetCashProvidedByUsedInFinancingActivitiesAbstract_ceac758c-0284-47cc-bd35-9a3dbf07afd2_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">Cash Provided by (Used in) Financing Activity, Including Discontinued Operation [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_NetCashProvidedByUsedInFinancingActivitiesAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.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_EffectiveIncomeTaxRateReconciliationNondeductibleExpense_3b3f72dd-d087-4632-8757-b9dfaf8d0065_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/2025/elts/us-gaap-2025.xsd#us-gaap_EffectiveIncomeTaxRateReconciliationNondeductibleExpense"/>
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    <link:label id="lab_us-gaap_IncomeLossFromContinuingOperationsAttributableToNoncontrollingEntity_60e74fe1-5703-4b5b-b304-50888d4952e9_negatedLabel_en-US" xlink:label="lab_us-gaap_IncomeLossFromContinuingOperationsAttributableToNoncontrollingEntity" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:type="resource" xml:lang="en-US">Less: Net loss from continuing operations attributable to noncontrolling interest</link:label>
    <link:label id="lab_us-gaap_IncomeLossFromContinuingOperationsAttributableToNoncontrollingEntity_label_en-US" xlink:label="lab_us-gaap_IncomeLossFromContinuingOperationsAttributableToNoncontrollingEntity" 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 Noncontrolling Interest</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncomeLossFromContinuingOperationsAttributableToNoncontrollingEntity" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_IncomeLossFromContinuingOperationsAttributableToNoncontrollingEntity"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_IncomeLossFromContinuingOperationsAttributableToNoncontrollingEntity" xlink:to="lab_us-gaap_IncomeLossFromContinuingOperationsAttributableToNoncontrollingEntity" xlink:type="arc" order="1"/>
    <link:label id="lab_codi_ActualDebtToEbitdaRatio_019b0d9b-ecce-7798-b4b4-7cd144fc4b7f_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>
    <link:label id="lab_codi_ActualDebtToEbitdaRatio_label_en-US" xlink:label="lab_codi_ActualDebtToEbitdaRatio" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Actual Debt To Ebitda Ratio</link:label>
    <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>
    <link:loc xlink:type="locator" xlink:label="loc_codi_ActualDebtToEbitdaRatio" xlink:href="codi-20250331.xsd#codi_ActualDebtToEbitdaRatio"/>
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    <link:label id="lab_us-gaap_MinorityInterestDisclosureTextBlock_f5b1b251-cc76-4a53-8d31-278f1413add5_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>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_MinorityInterestDisclosureTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_MinorityInterestDisclosureTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_MinorityInterestDisclosureTextBlock" xlink:to="lab_us-gaap_MinorityInterestDisclosureTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_SeriesCPreferredStockMember_3d7a19e5-9e2f-45dd-ae99-55c636251519_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>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SeriesCPreferredStockMember" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_SeriesCPreferredStockMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_SeriesCPreferredStockMember" xlink:to="lab_us-gaap_SeriesCPreferredStockMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_VariableRateDomain_bbb6cfb3-0e6c-4ec5-a568-3213700820a8_terseLabel_en-US" xlink:label="lab_us-gaap_VariableRateDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Variable Rate [Domain]</link:label>
    <link:label id="lab_us-gaap_VariableRateDomain_label_en-US" xlink:label="lab_us-gaap_VariableRateDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Variable Rate [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_VariableRateDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_VariableRateDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_VariableRateDomain" xlink:to="lab_us-gaap_VariableRateDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ScheduleOfFairValueAssetsAndLiabilitiesMeasuredOnRecurringBasisTableTextBlock_3c8621a3-276c-4f47-872f-cc6fe1550ee2_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfFairValueAssetsAndLiabilitiesMeasuredOnRecurringBasisTableTextBlock" 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 Recurring Basis</link:label>
    <link:label id="lab_us-gaap_ScheduleOfFairValueAssetsAndLiabilitiesMeasuredOnRecurringBasisTableTextBlock_label_en-US" xlink:label="lab_us-gaap_ScheduleOfFairValueAssetsAndLiabilitiesMeasuredOnRecurringBasisTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Schedule of Fair Value, Assets and Liabilities Measured on Recurring Basis [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfFairValueAssetsAndLiabilitiesMeasuredOnRecurringBasisTableTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ScheduleOfFairValueAssetsAndLiabilitiesMeasuredOnRecurringBasisTableTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ScheduleOfFairValueAssetsAndLiabilitiesMeasuredOnRecurringBasisTableTextBlock" xlink:to="lab_us-gaap_ScheduleOfFairValueAssetsAndLiabilitiesMeasuredOnRecurringBasisTableTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FinanceLeaseLiabilityNoncurrent_019b23d3-5ef6-7153-a914-9d552f37e3fa_terseLabel_en-US" xlink:label="lab_us-gaap_FinanceLeaseLiabilityNoncurrent" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Finance Lease, Liability, Noncurrent</link:label>
    <link:label id="lab_us-gaap_FinanceLeaseLiabilityNoncurrent_label_en-US" xlink:label="lab_us-gaap_FinanceLeaseLiabilityNoncurrent" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Finance Lease, Liability, Noncurrent</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FinanceLeaseLiabilityNoncurrent" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FinanceLeaseLiabilityNoncurrent"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FinanceLeaseLiabilityNoncurrent" xlink:to="lab_us-gaap_FinanceLeaseLiabilityNoncurrent" xlink:type="arc" order="1"/>
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    <link:label id="lab_codi_ThirdForbearanceAgreementMember_label_en-US" xlink:label="lab_codi_ThirdForbearanceAgreementMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Third Forbearance Agreement [Member]</link:label>
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    <link:label id="lab_codi_IndentureForbearanceAgreementMember_label_en-US" xlink:label="lab_codi_IndentureForbearanceAgreementMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Indenture forbearance agreement [Member]</link:label>
    <link:label id="lab_codi_IndentureForbearanceAgreementMember_documentation_en-US" xlink:label="lab_codi_IndentureForbearanceAgreementMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Indenture forbearance agreement</link:label>
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    <link:label id="lab_us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInYearTwo_9953ac3f-43f1-4b02-9dbe-53ea133fd027_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>
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    <link:label id="lab_us-gaap_NetCashProvidedByUsedInFinancingActivities_019cd45d-f7c5-4f13-8572-3318dae8ed00_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 financing activities</link:label>
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    <link:label id="lab_us-gaap_OperatingLeaseWeightedAverageDiscountRatePercent_b6ad39ba-b590-4165-95a8-c19e76d6d505_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">Weighted-average discount rate</link:label>
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    <link:label id="lab_us-gaap_PropertyPlantAndEquipmentTypeDomain_d97a5850-7246-46f3-bf81-a8e1c7611b68_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">Long-Lived Tangible Asset [Domain]</link:label>
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    <link:label id="lab_us-gaap_LandAndBuildingMember_45fd4b34-fd8a-4092-bbb7-46e3406b3626_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</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FiniteLivedIntangibleAssetsFutureAmortizationExpenseAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FiniteLivedIntangibleAssetsFutureAmortizationExpenseAbstract"/>
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    <link:label id="lab_us-gaap_DebtDisclosureAbstract_82316762-4b17-46df-9b11-7b677306c8e7_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/2025/elts/us-gaap-2025.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"/>
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    <link:label id="lab_us-gaap_NonoperatingIncomeExpenseAbstract_1eb1f9a4-4c71-48f9-9e00-af1b2b93b769_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>
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    <link:label id="lab_us-gaap_EffectiveIncomeTaxRateReconciliationTaxCredits_1ca489ab-cc37-4c28-8fca-0fff3d88cc1d_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_EffectiveIncomeTaxRateReconciliationTaxCredits" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Utilization of tax credits</link:label>
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    <link:label id="lab_us-gaap_IncomeTaxAuthorityNameAxis_label_en-US" xlink:label="lab_us-gaap_IncomeTaxAuthorityNameAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Income Tax Authority, Name [Axis]</link:label>
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    <link:label id="lab_us-gaap_AccountsReceivableGross_accd1033-c8ae-4914-9d56-c08f2c662c59_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>
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    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_GoodwillAndIntangibleAssetsDisclosureTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_GoodwillAndIntangibleAssetsDisclosureTextBlock"/>
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    <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/2025/elts/us-gaap-2025.xsd#us-gaap_FinanceLeaseInterestPaymentOnLiability"/>
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    <link:label id="lab_us-gaap_ConstructionInProgressGross_57c8eef3-7f44-4f33-99b3-05d025c2a2ed_terseLabel_en-US" xlink:label="lab_us-gaap_ConstructionInProgressGross" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Construction in process</link:label>
    <link:label id="lab_us-gaap_ConstructionInProgressGross_label_en-US" xlink:label="lab_us-gaap_ConstructionInProgressGross" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Construction in Progress, Gross</link:label>
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    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ConstructionInProgressGross" xlink:to="lab_us-gaap_ConstructionInProgressGross" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ScheduleOfGoodwillTextBlock_ac7396b7-018a-4c57-90c4-9efecbffda3c_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfGoodwillTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Summary of Reconciliation of Change in Carrying Value of Goodwill</link:label>
    <link:label id="lab_us-gaap_ScheduleOfGoodwillTextBlock_label_en-US" xlink:label="lab_us-gaap_ScheduleOfGoodwillTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Schedule of Goodwill [Table 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_ScheduleOfGoodwillTextBlock" xlink:to="lab_us-gaap_ScheduleOfGoodwillTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_BusinessAcquisitionProFormaEarningsPerShareBasic_8a1f7bef-fe89-4b3b-b0f3-52aa91255ced_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 Combination, Pro Forma Information, Pro Forma Earnings Per Share, Basic</link:label>
    <link:label id="lab_us-gaap_BusinessAcquisitionProFormaEarningsPerShareBasic_label_en-US" xlink:label="lab_us-gaap_BusinessAcquisitionProFormaEarningsPerShareBasic" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Business Combination, Pro Forma Information, Pro Forma Earnings Per Share, Basic</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_BusinessAcquisitionProFormaEarningsPerShareBasic" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_BusinessAcquisitionProFormaEarningsPerShareBasic"/>
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    <link:label id="lab_us-gaap_SubsequentEventsTextBlock_91bded9f-c135-4fce-bac7-ee13c94edc80_terseLabel_en-US" xlink:label="lab_us-gaap_SubsequentEventsTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Subsequent Events</link:label>
    <link:label id="lab_us-gaap_SubsequentEventsTextBlock_label_en-US" xlink:label="lab_us-gaap_SubsequentEventsTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Subsequent Events [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SubsequentEventsTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_SubsequentEventsTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_SubsequentEventsTextBlock" xlink:to="lab_us-gaap_SubsequentEventsTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OtherComprehensiveIncomeLossForeignCurrencyTransactionAndTranslationAdjustmentNetOfTax_0c556955-258c-42ed-a4fd-a58f70fdd534_terseLabel_en-US" xlink:label="lab_us-gaap_OtherComprehensiveIncomeLossForeignCurrencyTransactionAndTranslationAdjustmentNetOfTax" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Other Comprehensive Income (Loss), Foreign Currency Transaction and Translation Adjustment, Net of Tax</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OtherComprehensiveIncomeLossForeignCurrencyTransactionAndTranslationAdjustmentNetOfTax" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_OtherComprehensiveIncomeLossForeignCurrencyTransactionAndTranslationAdjustmentNetOfTax"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OtherComprehensiveIncomeLossForeignCurrencyTransactionAndTranslationAdjustmentNetOfTax" xlink:to="lab_us-gaap_OtherComprehensiveIncomeLossForeignCurrencyTransactionAndTranslationAdjustmentNetOfTax" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_SecurityExchangeName_4d693e2c-746a-45bc-b8d1-848181897d0d_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/2025/dei-2025.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_RelatedPartyTransactionPurchasesFromRelatedParty_21b5bc86-a4d1-44be-9df4-2ce793c9a945_terseLabel_en-US" xlink:label="lab_us-gaap_RelatedPartyTransactionPurchasesFromRelatedParty" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Related Party Transaction, Purchases from Related Party</link:label>
    <link:label id="lab_us-gaap_RelatedPartyTransactionPurchasesFromRelatedParty_label_en-US" xlink:label="lab_us-gaap_RelatedPartyTransactionPurchasesFromRelatedParty" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Related Party Transaction, Purchases from Related Party</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_RelatedPartyTransactionPurchasesFromRelatedParty" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_RelatedPartyTransactionPurchasesFromRelatedParty"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_RelatedPartyTransactionPurchasesFromRelatedParty" xlink:to="lab_us-gaap_RelatedPartyTransactionPurchasesFromRelatedParty" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_InterimPeriodCostsNotAllocableDomain_b6b11276-4fbc-40e1-8b12-deb379233bd9_terseLabel_en-US" xlink:label="lab_us-gaap_InterimPeriodCostsNotAllocableDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Interim Period, Costs Not Allocable [Domain]</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_InterimPeriodCostsNotAllocableDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_InterimPeriodCostsNotAllocableDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_InterimPeriodCostsNotAllocableDomain" xlink:to="lab_us-gaap_InterimPeriodCostsNotAllocableDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AccumulatedAmortizationDeferredFinanceCosts_7d26e8ba-6960-412a-8e86-1f14db8256da_terseLabel_en-US" xlink:label="lab_us-gaap_AccumulatedAmortizationDeferredFinanceCosts" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Accumulated amortization</link:label>
    <link:label id="lab_us-gaap_AccumulatedAmortizationDeferredFinanceCosts_593c8401-214d-49c7-8f90-039556a64dae_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_AccumulatedAmortizationDeferredFinanceCosts" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Accumulated Amortization, Debt Issuance Costs</link:label>
    <link:label id="lab_us-gaap_AccumulatedAmortizationDeferredFinanceCosts_label_en-US" xlink:label="lab_us-gaap_AccumulatedAmortizationDeferredFinanceCosts" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Accumulated Amortization, Debt Issuance Costs</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AccumulatedAmortizationDeferredFinanceCosts" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_AccumulatedAmortizationDeferredFinanceCosts"/>
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    <link:label id="lab_us-gaap_Liabilities_44998120-a513-41c8-82c4-ad3810c06a33_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>
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    <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_LineOfCreditFacilityMaximumBorrowingCapacity_afc1720f-4b16-46b7-a14d-be57fb6a4dfc_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>
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    <link:label id="lab_us-gaap_OtherLiabilitiesCurrent_2738e481-c21a-4f19-ad84-c59d80ecd1eb_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>
    <link:label id="lab_us-gaap_OtherLiabilitiesCurrent_label_en-US" xlink:label="lab_us-gaap_OtherLiabilitiesCurrent" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Other Liabilities, Current</link:label>
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    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OtherLiabilitiesCurrent" xlink:to="lab_us-gaap_OtherLiabilitiesCurrent" xlink:type="arc" order="1"/>
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    <link:label id="lab_codi_DistributorRelationsAndOtherMember_f247991c-016a-4a92-917a-f24b88e62baa_terseLabel_en-US" xlink:label="lab_codi_DistributorRelationsAndOtherMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Other contractual intangible assets</link:label>
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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_46611cad-399d-4984-93c0-238985a13b64_terseLabel_en-US" xlink:label="lab_codi_LuganoMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Lugano</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-20250331.xsd#codi_LuganoMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_codi_LuganoMember" xlink:to="lab_codi_LuganoMember" xlink:type="arc" order="1"/>
    <link:label id="lab_codi_DisposalGroupIncludingDiscontinuedOperationIntercompanyInterestExpenseExcludedfromIncomeLossfromDiscontinuedOperations_83e2f927-8678-407e-8add-672d3ab12fd7_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_codi_PaymentstoAcquireBusinessesNetofCashAcquiredandNetofTransactionsCosts_5626aedb-ea2a-423c-873f-90cee5ccb32c_terseLabel_en-US" xlink:label="lab_codi_PaymentstoAcquireBusinessesNetofCashAcquiredandNetofTransactionsCosts" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Payments to Acquire Businesses, Net of Cash Acquired and Net of Transactions Costs</link:label>
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    <link:label id="lab_us-gaap_StockIssuedDuringPeriodValueNewIssues_41fcbb7d-ce51-4dec-bab2-431631de5192_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_StockIssuedDuringPeriodValueNewIssues" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Stock Issued During Period, Value, New Issues</link:label>
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