Private and Strictly Confidential May 24, 2022 Corgi BidCo, Inc. c/o Clayton, Dubilier & Rice, LLC New York, NY 10152 Ladies and Gentlemen:

Exhibit (b)(4)

Confidential

Private and Strictly Confidential

May 24, 2022

Corgi BidCo, Inc.

▇/▇ ▇▇▇▇▇▇▇, ▇▇▇▇▇▇▇▇ & Rice, LLC

▇▇▇ ▇▇▇▇ ▇▇▇▇▇▇, ▇▇^▇▇ ▇▇▇▇▇

▇▇▇ ▇▇▇▇, ▇▇ ▇▇▇▇▇

Ladies and Gentlemen:

This letter agreement (this “Letter”) sets forth the commitments of TPG Partners VIII, L.P., a Delaware limited partnership (the “Investor”), subject to the terms and conditions set forth herein, to purchase, directly or indirectly, certain equity interests of Corgi BidCo, Inc., a newly formed Delaware corporation (“Parent”). It is contemplated that, pursuant to that certain Agreement and Plan of Merger (as amended, restated, amended and restated, supplemented or otherwise modified from time to time, the “Transaction Agreement”), dated as of the date hereof, by and among Parent, Corgi Merger Sub, Inc., a Delaware corporation and direct wholly-owned subsidiary of Parent (“Merger Sub”), and Covetrus, Inc., a Delaware corporation (the “Company”), at the Closing of the transactions contemplated thereby (the “Transaction”), Merger Sub will be merged with and into the Company and the separate corporate existence of Merger Sub shall thereupon cease (the “Merger”), with the Company being the surviving corporation of such Merger and the direct, wholly-owned subsidiary of Parent. Capitalized terms used and not otherwise defined herein shall have the meanings ascribed to such terms in the Transaction Agreement.

1. Commitments. The Investor hereby irrevocably and unconditionally commits (its “Commitment”), subject to the terms and conditions set forth herein, that, at or prior to the Closing, it shall punctually purchase, or shall cause the punctual purchase of, directly or indirectly through one or more intermediate entities, equity securities of Parent, with immediately available funds, at the same price per equity security and of the same class as the equity securities purchased by ▇▇▇▇▇▇▇, Dubilier & Rice Fund XI, L.P., a Cayman Islands exempted limited partnership, and TPG Healthcare Partners, L.P., a Delaware limited partnership (together, the “Other Investors”) pursuant to those certain letter agreements, dated as of the date hereof, executed by the Other Investors in favor of Parent (the “Other Investors Equity Commitment Letters”), with an aggregate purchase price not to exceed $526,839,600.00 (the “Cap”). Notwithstanding anything to the contrary in this Letter, this Letter may not be enforced against the Investor without giving effect to the Cap. The Commitment, subject to the Cap, together with the proceeds of the Other Investors Equity Financing (as defined herein) and the Debt Financing will be solely used to (a) fund all Merger Consideration required to be paid by Parent at the Closing pursuant to Article 3 of the Transaction Agreement and (b) pay indebtedness, fees and expenses expressly required to be paid by Parent pursuant to the Transaction Agreement (the “Transaction Expenses”). For purposes of this Letter, (i) the “Other Investors Equity Financing” means the direct or indirect purchase of equity securities of Parent by the Other Investors pursuant to, and in accordance with, the terms of the Other Investors Equity Commitment Letters, and (ii) the “Other Investors’ Commitments” means the Commitment (as defined in the Other Investors Equity Commitment Letters) of each of the Other Investors.

2. Conditions. The Investor’s Commitment shall be subject to (a) the execution and delivery of the Transaction Agreement by all parties thereto, (b) the satisfaction or waiver by Parent and Merger Sub of each of the conditions to Parent’s and Merger Sub’s obligations to effect the Closing set forth in Article 7 of the Transaction Agreement (in each case, other than any conditions that by their nature are to be satisfied at the Closing, but subject to the prior or substantially concurrent satisfaction or waiver of such conditions), (c) the substantially contemporaneous, or prior, funding of the Debt Financing (or, if applicable any Alternative Financing) in accordance with the terms of the applicable Commitment Letter at the Closing if each of the Commitment and the Other Investors’ Commitments is funded and (d) the substantially simultaneous consummation of the Closing in accordance with the terms of the Transaction Agreement. If the amount required to be paid by Parent pursuant to the Transaction Agreement is less than the aggregate sum of the Investor’s Commitment as funded and the Other Investors’ Commitments as funded, solely to the extent Parent does not require the full amount of the Commitment and the Other Investors’ Commitments to fund (a) the Merger Consideration required to be paid by Parent at the Closing pursuant to Article 3 of the Transaction Agreement and (b) pay the Transaction Expenses, the Investor’s Commitment hereunder and the Other Investors’ Commitments will each be accordingly reduced with such reduction allocated to the Investor’s Commitment and the Other Investors’ Commitments on a pro rata basis; provided that (x) it will thereafter be possible for Parent to satisfy payments (and without breaching the terms of the Debt Commitment Letter or causing the failure of any of the conditions set forth therein) with the Investor and the Other Investors contributing less than the full amount of the Commitment and the Other Investors’ Commitments, respectively and (y) such amounts referred to in the foregoing clauses (a) and (b) are actually funded at Closing and not returned.

3. Limited Guarantee. Concurrently with the execution and delivery of this Letter, the Investor and the Other Investors are each executing and delivering to the Company a limited guarantee dated as of the date hereof and related to the performance of certain of Parent’s payment obligations under the Transaction Agreement (the “Limited Guarantees”). Other than with respect to the Company’s rights pursuant to clause (b) of Section 5 hereof and the Company’s rights pursuant to clause (b) of Section 5 of the Other Investors Equity Commitment Letters, the Company’s right to assert any Retained Claim (as defined in the Limited Guarantees) against any Non-Recourse Party (as defined in the Limited Guarantee) against which such Retained Claim may be asserted pursuant to Section 8 of the Limited Guarantees and the Company’s remedies against the Investor and the Other Investors under their applicable Limited Guarantee shall be, and are intended to be, the sole and exclusive direct or indirect remedies available to the Company and its security holders and Affiliates against the Investor, the Other Investors or any other Non-Recourse Party in respect of any liabilities or obligations arising under, or in connection with, this Letter, the Other Investors Equity Commitment Letters, the Limited Guarantees, the Transaction Agreement or the transactions contemplated thereby or the negotiation hereof or thereof, including breaches hereof or thereof, whether or not such breach is caused by the Investor’s breach of its obligations under this Letter.

-2-

4. Parties in Interest; Third Party Beneficiaries. The parties hereto hereby agree that their respective agreements and obligations set forth herein are solely for the benefit of the other party hereto and its respective successors and permitted assigns, in accordance with and subject to the terms of this Letter, and this Letter is not intended to, and does not, confer upon any Person other than the parties hereto and their respective successors and permitted assigns any benefits, rights or remedies under or by reason of, or any rights to enforce or cause Parent to enforce, the obligations set forth herein; provided, that (a) the Company is an express third-party beneficiary of, and shall have the enforcement rights provided in, clause (b) of Section 5 of this Letter, and (b) any Non-Recourse Party may rely on and enforce the provisions of Section 6 hereof.

5. Enforceability. This Letter may only be enforced by (a) Parent at the direction of the Investor or (b) the Company pursuant to the Company’s right to seek specific performance of Parent’s obligation to enforce the Investor’s obligation to fund its Commitment in accordance with the terms hereof, pursuant to, and subject to, and solely in accordance with, the terms and conditions of Section 9.13 of the Transaction Agreement and the rights set forth herein; provided that, this Letter may only be enforced by Parent in accordance with clause (a) above or the Company in accordance with clause (b) above if Parent or the Company, as applicable, is also seeking the enforcement of the obligations of the Other Investors under, and in accordance with, the Other Investors Equity Commitment Letters. Neither Parent’s creditors nor any other Person (other than the Company to the extent provided herein) shall have any right to enforce this Letter or to cause Parent to enforce this Letter. For the avoidance of doubt, and notwithstanding anything to the contrary herein, nothing in this Letter shall affect the right of Investor, Other Investors or Parent to enforce any terms of that certain Interim Investors Agreement, executed as of the date hereof, by and among the Investor, the Other Investors and Parent (the “Interim Investors Agreement”).

6. No Modification; Entire Agreement. This Letter may not be amended or otherwise modified without the prior written consent of Parent, the Investor and the Company. Together with the Transaction Agreement, the Limited Guarantee, the Confidentiality Agreement, the Interim Investors Agreement, and this Letter constitutes the sole agreement, and supersedes all prior agreements, understandings and statements, written or oral, between the Investor or any of its Affiliates, on the one hand, and Parent or any of its Affiliates, on the other, with respect to the transactions contemplated hereby. Except as expressly permitted in Section 11 hereof, no transfer of any rights or obligations hereunder shall be permitted without the consent of Parent, the Investor and the Company. Any transfer in violation of the preceding sentence shall be null and void.

7. Governing Law; Jurisdiction; Venue; Waiver of Jury Trial.

(a) This Letter and all Actions (whether based on contract, tort or otherwise) arising out of or relating to this Letter, any of the transactions contemplated by this Letter, or any of the acts or omissions of Parent, the Investor or the Company in the negotiation, administration, performance or enforcement hereof or thereof shall be governed and construed in accordance with the laws of the State of Delaware without giving effect to the principles of conflicts of law thereof or of any other jurisdiction which would require the application of the laws of any other jurisdiction.

-3-

(b) Each party hereto submits to the exclusive jurisdiction of the state courts located in Wilmington, Delaware or the courts of the United States located in Wilmington, Delaware in respect of any action seeking to enforce any provision of, or based on any matter arising out of or in connection with, this Letter or the transactions contemplated hereby and waives, and agrees not to assert, any defense in any action for the interpretation or enforcement of this Letter and any related agreement, certificate or other document delivered in connection herewith, that they are not subject thereto or that such action may not be brought or is not maintainable in such courts or that this Letter may not be enforced in or by such courts or that their property is exempt or immune from execution, that the action is brought in an inconvenient forum, or that the venue of the action is improper. Service of process with respect thereto may be made upon any party to this agreement by mailing a copy thereof by registered or certified mail, postage prepaid, to such party at its address as provided in Section 6 of the Investor’s Limited Guarantee.

(c) EACH PARTY HERETO HEREBY IRREVOCABLY WAIVES, TO THE FULLEST EXTENT PERMITTED BY APPLICABLE LAW, ANY RIGHT IT MAY HAVE TO A TRIAL BY JURY WITH RESPECT TO THIS LETTER AND ALL ACTIONS OR CLAIMS (WHETHER BASED ON ANY DISPUTE IN CONTRACT, TORT OR OTHERWISE) ARISING OUT OF OR RELATING TO THIS LETTER, ANY OF THE TRANSACTIONS CONTEMPLATED BY THIS LETTER OR ANY OF THE ACTS OR OMISSIONS OF PARENT, THE INVESTOR OR THE COMPANY IN THE NEGOTIATION, ADMINISTRATION, PERFORMANCE OR ENFORCEMENT HEREOF OR THEREOF, AS THE CASE MAY BE. EACH PARTY HERETO (I) CERTIFIES THAT NO REPRESENTATIVE, AGENT OR ATTORNEY OF ANY OTHER PARTY HERETO HAS REPRESENTED, EXPRESSLY OR OTHERWISE, THAT SUCH OTHER PARTY HERETO WOULD NOT, IN THE EVENT OF LITIGATION, SEEK TO ENFORCE THE FOREGOING WAIVER AND (II) ACKNOWLEDGES THAT IT AND THE OTHER PARTIES HERETO HAVE BEEN INDUCED TO ENTER INTO THIS LETTER BY, AMONG OTHER THINGS, THE MUTUAL WAIVERS AND CERTIFICATIONS IN THIS SECTION 7(C).

8. Counterparts. This Letter shall not be effective until it has been executed and delivered by all parties hereto. This Letter may be executed in any number of counterparts (including by facsimile or by .pdf delivered via email), each such counterpart when executed being deemed to be an original instrument, and all such counterparts shall together constitute one and the same agreement.

9. Confidentiality. This Letter shall be treated as confidential and is being provided to Parent solely in connection with the Transaction. This Letter may not be used, circulated, quoted or otherwise referred to in any document (other than the Transaction Agreement, the Limited Guarantees, the Other Investors Equity Commitment Letters, the Debt Commitment Letter or any other ancillary agreements entered into in connection with the Transaction) by

-4-

Parent except with the prior written consent of the Investor in each instance; provided, that (a) this Letter may be provided to the Company (so long as the Company agrees to keep, and agrees to cause its directors, officers, employees, partners, advisors and other representatives to keep, this Letter confidential) and (b) no such written consent is required for any disclosure of the existence of this Letter (i) to the extent required by applicable Law (provided, that Parent or the Company, as applicable, will provide the Investor an opportunity to review such required disclosure in advance of such public disclosure being made), (ii) to Parent’s or the Company’s Representatives who need to know of the existence or terms of this Letter (so long as such Representatives agree to keep, and agrees to cause their directors, officers, employees and partners, this Letter confidential) or (iii) in connection with any litigation or Action related to Transaction Agreement, the Limited Guarantees, the Other Investors Equity Commitment Letters, the Debt Commitment Letter or any other ancillary agreements entered into in connection with the Transaction.

10. Termination. The obligation of the Investor under or in connection with this Letter will terminate automatically and immediately upon the earliest to occur of (a) the Closing and the funding of the Commitment (at which time all such obligations shall be discharged), (b) the termination of the Transaction Agreement pursuant to its terms (unless the Company shall have previously commenced an action pursuant to clause (b) of Section 5 hereof, in which case this Letter shall terminate upon the final, non-appealable resolution of such action and satisfaction by the Investor of any obligations finally determined or agreed to be owed by the Investor in respect of the payment obligations of Parent consistent with the terms hereof), (c) the Company or any of its controlled Affiliates, or any Person claiming by, through or for the benefit of any of the foregoing, accepting all or any portion of the Company Termination Fee pursuant to the Transaction Agreement or accepting any payment from the Guarantor (as defined in the Limited Guarantee) under the Limited Guarantee in respect of such obligations, (d) the Company or any of its controlled Affiliates asserting in writing a claim against the Investor or any Non-Recourse Party under or in connection with either the Limited Guarantee or the Transaction Agreement other than the Company asserting any Retained Claim against any Non-Recourse Party against which such Retained Claim may be asserted pursuant to Section 8 of the Limited Guarantee and (e) the termination of the Other Investors Equity Commitment Letters.

11. No Assignment. The Commitment evidenced by this Letter shall not be assignable, in whole or in part, by Parent without the Investor’s and the Company’s prior written consent, and the granting of such consent in a given instance shall be solely in the discretion of the Investor and the Company, as applicable, and, if granted, shall not constitute a waiver of this requirement as to any subsequent assignment. Investor may assign all or a portion of its obligations to fund the Commitment to its Affiliates or affiliated funds or to entities governed by one of its Affiliates or affiliated funds subject to the prior written consent of the Company; provided, that any permitted assignment shall not relieve Investor of its obligations under this Letter. Any purported assignment of this Letter or the Commitment in contravention of this Section 11 shall be void and of no force and effect. The Investor and Parent shall give written notice to the Company of any assignment pursuant to this paragraph that is effected prior to Closing as promptly as practicable thereafter (and in no event more than two (2) Business Days thereafter).

-5-

12. Representations and Warranties. The Investor hereby represents and warrants to Parent that: (a) it has all limited partnership power and authority to execute, deliver and perform this Letter; (b) the execution, delivery and performance of this Letter by it has been duly and validly authorized and approved by all necessary limited partnership or other organizational action by it and no other proceedings or actions on the part of it are necessary therefor; (c) this Letter has been duly and validly executed and delivered by it and constitutes a valid and legally binding obligation of it, enforceable against it in accordance with the terms of this Letter; (d) its Commitment is less than the maximum amount that it is permitted to invest in any one portfolio investment pursuant to the terms of its constituent documents or otherwise; (e) it has, and will maintain for so long as this Letter is in effect, uncalled capital commitments or access to available funds in excess of the sum of its Commitment hereunder plus the aggregate amount of all other commitments and obligations it currently has outstanding; (f) all consents, approvals, authorizations, permits of, filings with and notification to, any governmental authority necessary for the due execution, delivery and performance of this Letter by the Investor have been obtained or made and all conditions thereof have been duly complied with, and no other action by, and no notice to or filing with, any governmental authority or regulatory body is required in connection with the execution, delivery or performance of this Letter; and (g) the execution, delivery and performance by the Investor of this Letter do not (i) violate the organizational documents of the Investor, (ii) violate any applicable law or judgment or (iii) result in any violation of, or default (with or without notice or lapse of time or both) under, or give rise to a termination, cancellation or acceleration of any obligation or to the loss of any benefit under, any material contract to which it is a party.

[Remainder of the page intentionally left blank – signature page follows]

-6-