Exhibit 99.(d)(x)

EXECUTION VERSION

March 2, 2026

To:

Stallion Intermediate Corporation

c/o Welsh, Carson, Anderson & Stowe

599 Lexington Avenue, Suite 1800

New York, New York 10022

Attention: Ting Gu

Greetings:

This letter agreement (this “Agreement”) sets forth the commitment (the “Commitment”) of WCAS XIV, L.P., a Delaware limited partnership (the “Fund”), to purchase, directly or indirectly, in each case, on the terms and subject to the conditions contained herein, certain equity securities of Stallion Intermediate Corporation, a Delaware corporation (“Parent”), or make capital contributions to Parent on the terms and subject to the conditions contained herein. It is contemplated that pursuant to that certain Agreement and Plan of Merger (as amended, restated, supplemented or otherwise modified from time to time, the “Merger Agreement”) dated as of the date hereof, by and among Parent, Stallion Merger Sub Corporation, a Delaware corporation and wholly owned subsidiary of Parent (“Merger Sub”), and Select Medical Holdings Corporation, a Delaware corporation (the “Company”), Merger Sub will merge with and into the Company, with the Company as the surviving corporation (the “Contemplated Transaction”). Capitalized terms used and not otherwise defined herein shall have the meanings ascribed to such terms in the Merger Agreement (to the extent such terms are defined therein).

1.            Commitments. The Fund hereby commits (the “Commitment”) to purchase, or to cause one or more of its Affiliates to purchase, at or prior to the Closing, directly or indirectly, on the terms and subject to the conditions set forth herein, equity securities of Parent for an aggregate purchase price equal to the $880,000,000 (the “Commitment Amount”), solely for the purpose of funding, and to the extent necessary to fund, all amounts required to be paid by Parent as of the Closing pursuant to Sections 4.2(a) and 4.3 of the Merger Agreement, together with any related fees and expenses Parent is required to pay at the Closing pursuant to the terms of the Merger Agreement (the “Aggregate Required Amount”); provided that, in no event will the Fund and/or its permitted assignees have any obligation under any circumstance to contribute to, purchase equity securities of, or otherwise provide funds to, Parent in excess of the Commitment Amount (and in no event will the Fund (together with its permitted assigns), be under any obligation under any circumstances to provide an aggregate amount of funds of more than the Aggregate Required Amount). The amount to be funded by the Fund under this Agreement will be reduced (on a dollar-for-dollar basis) at or immediately prior to Closing solely in the event that Parent does not require all of the Commitment to pay the Aggregate Required Amount by reason of Parent having obtained funds from other sources (including cash on hand, debt financing sources or any rollover and/or equity co-investment) that are readily available to Parent to pay all amounts required to be paid by Parent as of the Closing pursuant to Sections 4.2(a) and 4.3 of the Merger Agreement, together with any related fees and expenses Parent is required to pay at the Closing pursuant to the terms of the Merger Agreement.

2.            Conditions. The Fund’s obligation to fund the Commitment shall be subject to the following conditions: (a) all of the conditions set forth in Sections 8.1 and 8.2 of the Merger Agreement have been and continue to be satisfied or waived (other than those that, by their nature, are to be satisfied at the Closing; provided that those conditions could be satisfied if the Closing were to occur), (b) the Company has irrevocably confirmed by written notice to Parent that (x) all conditions set forth in Section 8.3 of the Merger Agreement have been satisfied (other than those that, by their nature, are to be satisfied at the Closing) or that they would be willing to waive any unsatisfied conditions in Section 8.3 of the Merger Agreement and (y) that the Company is ready, willing, and able to consummate the Closing if specific performance is granted and the Debt Financing were funded, (c) the Debt Financing has been funded or will be funded at the Closing (in each case, in accordance with the terms and conditions thereof), and (d) the substantially simultaneous consummation of the Closing in accordance with the terms of the Merger Agreement.

3.            Acknowledgement. The Fund acknowledges and agrees that if the conditions described in Section 2 above are satisfied, the Company may seek specific performance of the Fund’s obligation to fund the Commitment hereunder pursuant to (and on the terms and subject to the conditions of) Section 10.5 of the Merger Agreement (the “Specific Performance Right”).

4.            Confidentiality. This Agreement shall be treated as confidential and is being provided to Parent solely in connection with the Contemplated Transaction. This Agreement may not be used, circulated, delivered, quoted or otherwise referred to in any document (other than the Merger Agreement and the Limited Guaranty by the Fund, dated on or about the date hereof (the “Limited Guaranty”), and any debt financing documentation) by the Company or any other third party beneficiary hereunder or its respective Affiliates except with the prior written consent of Parent and the Fund in each instance; provided, that no such written consent is required for any disclosure of this Agreement to (a) the extent required by applicable Law (or the rules of any stock exchange or self-regulatory organization) or in connection with the enforcement of rights under this Agreement, the Merger Agreement or the transactions contemplated hereby and thereby or (b) representatives of Parent, the Company or the Fund who need to know of the existence of this Agreement in connection with the transactions contemplated hereby so long as such representatives agree to keep such information confidential on terms substantially identical to the terms contained in this Section 4.

5.            Representations and Warranties. The Fund hereby represents and warrants to Parent that (a) it has all requisite limited partnership or similar power and authority to execute, deliver and perform this Agreement, (b) the execution, delivery and performance of this Agreement by the Fund has been duly and validly authorized and approved by all necessary organizational action by it, (c) this Agreement has been duly and validly executed by the Fund and (assuming due execution and delivery of this Agreement and the Merger Agreement by all the other parties hereto and thereto) constitutes a legal, valid and binding obligation of the Fund, enforceable against the Fund in accordance with its terms, subject to the Bankruptcy and Equity Exception, (d) the Fund (or its relevant Affiliate) will have uncalled capital commitments or has other available funds in excess of the Commitment Amount hereunder plus the aggregate amount of all other commitments and obligations it currently has outstanding, and (e) the execution, delivery and performance by the Fund of this Agreement do not violate the Fund’s agreement of limited partnership or other organizational documents.

6.            Parties in Interest; Enforceability. This Agreement shall only be binding upon the parties hereto and their respective successors and permitted assigns. This Agreement is not intended to, and does not, confer upon any other Person any benefits, rights or remedies; provided that (a) the Company shall have the right to seek specific performance to cause the Fund to fund an amount up to the Commitment Amount to Parent as described in Section 3 of this Agreement and (b) each Non-Recourse Party (as defined below) may rely upon and enforce the provisions of Section 13 hereof. Neither Parent’s creditors (other than the Company to the extent provided herein) nor any Person claiming by, through or on behalf or for the benefit of Parent or the Company, or any Affiliate shall have any right to enforce this Agreement or to cause Parent to enforce this Agreement. The Company hereby agrees that the Specific Performance Right shall be the sole and exclusive remedy with respect to any breach by the Fund of this Agreement and that, other than as expressly contemplated by the Limited Guaranty, it may not seek or accept any other form of relief that may be available for breach of this Agreement (including monetary, punitive, indirect, special, consequential or any other damages or remedies).

7.            Amendment. Except as set forth in Section 12, no amendment, modification or waiver of any provision of this Agreement will be enforceable unless approved in writing by Parent, the Fund and the Company.

8.            Termination. This Agreement and all obligations of the Fund to fund the Commitment will terminate automatically and immediately upon the earliest to occur of (a) the Closing (at which time all such obligations shall be discharged), (b) the assertion by the Company or any of its Affiliates (other than any Rollover Holder) of any claim against the Fund or any Non-Recourse Party (other than claims (i) against the Fund pursuant to, and in accordance with, this Agreement, (ii) against Parent pursuant to, and in accordance with, the Merger Agreement, (iii) against the Fund pursuant to the Confidentiality Agreement, and (iv) against the Fund pursuant to, and in accordance with, the Limited Guaranty), (c) payment of the Parent Termination Fee pursuant to the Merger Agreement or the Limited Guaranty, or (d) the valid termination of the Merger Agreement in accordance with its terms. Upon termination of this Agreement, neither the Fund nor any of its respective assigns shall have any further obligations or liabilities hereunder, but such termination shall not relieve the Fund of any of its obligations under the Limited Guaranty. Notwithstanding anything set forth in this Section 8, Section 4, and Sections 7 through 14 shall survive indefinitely (subject to the applicable statute of limitations) following the termination of this Agreement.

9.            Headings; Construction. The descriptive headings contained in this Agreement are for convenience of reference only and are not intended to be part of or to affect the meaning or interpretation of this Agreement. The language used in this Agreement shall be deemed to be the language chosen by the parties to express their mutual intent, and no rule of strict construction shall be applied against any Person.

10.          Governing Law and Venue; Waiver of Jury Trial. The provisions of Section 10.4 (Governing Law and Venue; Waiver of Jury Trial) and 10.12 (Interpretation and Construction) of the Merger Agreement are incorporated herein mutatis mutandis as if fully set forth herein and made a part of this Agreement.

11.          Entire Agreement; Integration. Together with the Merger Agreement, the Limited Guaranty and the Confidentiality Agreement, this Agreement constitutes the entire agreement of Parent, the Fund and the Company with respect to the subject matter hereof, and supersedes all prior agreements and understandings, both written or oral, between the Fund or any of its Affiliates, on the one hand, and Parent or any of its Affiliates, on the other, with respect to the subject matter hereof.

12.          No Assignment. Neither this Agreement nor any Commitment evidenced by this Agreement shall be assignable without the prior written consent of Parent, the Fund and the Company; provided, however, that, without the consent of the Company, the Fund may assign all or any portion of the Commitment Amount hereunder to any Affiliate of the Fund or any other Person providing equity financing to Parent; provided, however, that any such assignment shall not relieve the Fund of its obligations hereunder unless and to the extent actually performed. Any purported assignment of this Agreement or all or any portion of the Commitment Amount in contravention of this Section 12 shall be void.

13.          No Recourse against Affiliates, etc. Notwithstanding anything that may be expressed or implied in this Agreement, by their acceptance hereof each of Parent and the Company covenants, acknowledges and agrees for themselves and their respective Affiliates, that (a) no Person other than the Fund (and its successors and assignees) shall have any obligation hereunder, (b) notwithstanding that the Fund is a limited partnership, no recourse hereunder or under any documents or instruments delivered in connection herewith may be sought or had against any Non-Recourse Party, whether by the enforcement of any judgment or assessment or by any legal or equitable proceeding or by virtue of any statute, regulation or other applicable Law, and (c) no liability whatsoever will attach to, be imposed on or otherwise be incurred by any Non-Recourse Party in connection with this Agreement or any documents or instrument delivered in connection herewith or in respect of any oral representations made or alleged to be made in connection herewith or therewith for any obligation of the Fund under this Agreement or in connection with the Commitment, or any claim (whether at law or equity or in tort, contract or otherwise) based on, in respect of, or by reason of this Agreement or the Commitment; provided, however, that nothing in this Section 13 is intended or shall be construed to limit the obligations of the Guarantor under the Limited Guaranty or Parent under the Merger Agreement. Notwithstanding anything to the contrary herein, this Section 13 shall survive the termination of this Agreement. For the purposes of this Agreement, “Non-Recourse Party” means, with respect to any party to this Agreement, any of such party’s former, current and future equity holders, controlling persons, directors, officers, employees, agents, representatives, Affiliates, members, managers, general or limited partners, or assignees (or any former, current or future equity holder, controlling person, director, officer, employee, agent, representative, Affiliate, member, manager, general or limited partner, or assignee of the foregoing); provided, that for the avoidance of doubt, no party to this Agreement shall be considered a Non-Recourse Party.

14.          Counterparts. This Agreement may be executed in one or more counterparts, all of which shall constitute one and the same instrument. Any such counterpart, to the extent delivered by means of electronic transmission (including by pdf, .tif, .gif, .jpeg or similar attachment to electronic mail (any such delivery, an “Electronic Delivery”)) shall be treated in all manner and respects as an original executed counterpart and shall be considered to have the same binding legal effect as if it were the original signed version thereof delivered in person. At the request of a party, the other party shall re-execute the original form of this Agreement and deliver such form to such requesting party. No party shall raise the use of Electronic Delivery to deliver a signature or the fact that any signature or agreement or instrument was transmitted or communicated through the use of Electronic Delivery as a defense to the formation of a contract, and each such party forever waives any such defense. Minor variations in the form of the signature page, including footers from earlier versions of this Agreement or any such other document, will be disregarded in determining a party’s intent or the effectiveness of such signature.

15.          Relationships of the Parties. Each party acknowledges and agrees that (a) this Agreement is not intended to, and does not, create any agency, partnership, fiduciary or joint venture relationship between any of the parties hereto and neither this Agreement nor any other document or agreement entered into by any party hereto relating to the subject matter hereof shall be construed to suggest otherwise and (b) the obligations of the Fund under this Agreement are solely contractual in nature.

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[Signature Page to Equity Commitment Letter]

Agreed to and accepted:

[Signature Page to Equity Commitment Letter]