Exhibit 23.4

CONSENT OF INDEPENDENT REGISTERED PUBLIC ACCOUNTING FIRM

We hereby consent to the incorporation by reference in the Registration Statements on Form S-1 and Form S-3 of Adagio Medical Holdings, Inc. of our report dated March 26, 2026, which includes an explanatory paragraph regarding Adagio Medical Holdings, Inc.’s ability to continue as a going concern, relating to the consolidated balance sheets of Adagio Medical Holdings, Inc. as of December 31, 2025 and 2024, and the related consolidated statements of operations and comprehensive loss, stockholders’ equity (deficit), and cash flows for the year ended December 31, 2025 and the periods July 31 to December 31, 2024 (Successor) and January 1 to July 30, 2024 (Predecessor), appearing in the Company’s Annual Report on Form 10-K for the years ended December 31, 2025 and 2024.

We also consent to the reference to us under the caption “Experts” in the Registration Statements.

WithumSmith+Brown, PC

Whippany, New Jersey

March 31, 2026