Additional Proxy Soliciting Materials (Form DEFA14A)

SCHEDULE 14A

Proxy Statement Pursuant to Section 14(a) of the Securities Exchange Act of 1934

(Amendment No.__)

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Preliminary Proxy Statement

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Definitive Proxy Statement

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Definitive Additional Materials

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Soliciting Material under § 240.14a-12

Adagio Medical Holdings, Inc.

(Name of Registrant as Specified in Its Charter)

_____________________________________________________________________

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26051 Merit Circle, Suite 102

Laguna Hills, CA

SUPPLEMENT TO PROXY STATEMENT FOR THE 2025 ANNUAL MEETING OF STOCKHOLDERS

To Our Stockholders:

This proxy statement supplement, dated December 11, 2025 (this "Supplement"), supplements the definitive proxy statement on Schedule 14A of Adagio Medical Holdings, Inc. (the "Company"), dated November 4, 2025 (the "Proxy Statement"), for the Company's 2025 Annual Meeting of Stockholders to be held on December 15, 2025 (the "Annual Meeting"). This Supplement has been prepared to provide the Company's stockholders with information about certain changes on the Company's Board of Directors (the "Board") that occurred subsequent to the filing of the Proxy Statement.

THIS SUPPLEMENT SHOULD BE READ IN CONJUNCTION WITH THE PROXY STATEMENT.

Appointment of Sean Salmon as a Class II Director

On December 11 2025, the Board, based on the recommendation of the Nominating and Corporate Governance Committee of the Board, appointed Sean Salmon to the Board, effective December 11, 2025. Mr. Salmon was appointed as a Class II director for a term expiring at the Company's 2026 Annual Meeting of Stockholders or until his successor is duly elected or qualified. Mr. Salmon has been appointed to each of the Audit Committee and the Compensation Committee of the Board.

The Board affirmatively determined that Mr. Salmon is independent within the meaning of Nasdaq Stock Market ("Nasdaq") listing standards. Following Mr. Salmon's appointment, six out of the seven directors are independent per Nasdaq listing standards applicable to boards of directors in general.

Mr. Salmon will receive compensation consistent with that received by the Company's other non-employee directors, pursuant to the non-employee director compensation policy, as described under the caption "Non-Employee Director Compensation" in the Proxy Statement. The Company has also entered into its standard form of indemnification agreement with Mr. Salmon.

Mr. Salmon, age 60, served as Executive Vice President and President of Medtronic's Cardiovascular Portfolio from January 2021 to September 2025. Mr. Salmon previously served as Medtronic's Executive Vice President and President of the Diabetes Operating Unit (previously known as Diabetes Group) from October 2019 to May 2022. Prior to that, he served as Senior Vice President and President of Coronary and Structural Heart Business within the Cardiac and Vascular Group of Medtronic beginning in July 2014, having held other positions of increasingly responsibility with Medtronic since 2004. Prior to joining Medtronic, Mr. Salmon worked at CR Bard and Johnson & Johnson. Mr. Salmon holds a B.S. degree from Boston University and an M.B.A. from the Kellogg School of Management at Northwestern University.

As of December 10, 2025, Mr. Salmon did not beneficially own any shares of the Company's common stock.

There is no arrangement or understanding between Mr. Salmon and any other person pursuant to which he was appointed as a director. There are no transactions in which Mr. Salmon has an interest requiring disclosure under Item 404(a) of Regulation S-K.

Voting Matters

The Board changes described above do not impact Proposal 1, Election of Directors, to be voted on at the Annual Meeting. Mr. Salmon is not a Class I nominee for the Annual Meeting, and you are not being asked to vote on or ratify the appointment of Mr. Salmon.

Except as specifically supplemented by the information contained herein, this Supplement does not modify any other information set forth in the Proxy Statement. The Proxy Statement, together with this Supplement, have been filed with the SEC and are also available at www.proxyvote.com.

Please note that any proxy card or voting instruction form that you may have received has not changed and may still be used to vote your shares in connection with the Annual Meeting. If you have already submitted your vote, you do not need to take any further action. Information on how to vote your shares and how to change your vote or revoke your proxy is contained in the Proxy Statement. The Company urges stockholders to vote their shares prior to the Annual Meeting by using one of the methods described in the Proxy Statement.

SIGNATURE

Pursuant to the requirements of the Securities Exchange Act of 1934, the registrant has duly caused this report to be signed on its behalf by the undersigned hereunto duly authorized.

	ADAGIO MEDICAL HOLDINGS, INC.
Date: December 11, 2025	By:	/s/ Deborah Kaster
		Deborah Kaster
		Chief Financial Officer and Chief Business Officer