Exhibit 2.1

CONSENT AND AMENDMENT NO. 1

TO BUSINESS COMBINATION AGREEMENT

This CONSENT AND AMENDMENT NO. 1 to the BUSINESS COMBINATION AGREEMENT, dated as of June 25, 2024 (this “Consent and Amendment”), is made by and between ARYA Sciences Acquisition Corp IV, a Cayman Islands exempted company (“ARYA”) and Adagio Medical, Inc., a Delaware corporation (the “Company”). ARYA and the Company shall each be referred to herein from time to time individually as a “Party” and collectively as the “Parties”.

RECITALS:

WHEREAS, ARYA, Aja Holdco, Inc., a Delaware corporation, Aja Merger Sub 1, a Cayman Islands exempted company, the Company, and Aja Merger Sub 2, Inc., a Delaware corporation, entered into that certain Business Combination Agreement, dated as of February 13, 2024 (the “Business Combination Agreement”);

WHEREAS, pursuant to Section 5.1 of the Business Combination Agreement, ARYA has consent rights with respect to certain actions of the Company between the date of the Business Combination Agreement and the Closing or the earlier termination of the Business Combination Agreement;

WHEREAS, the Company intends to enter into an exchange agreement (the “Exchange Agreement”) with RA Capital Healthcare Fund, L.P., a Delaware limited partnership (“RA Capital”), pursuant to which, RA Capital will exchange a certain number of its existing Company Series E Preferred Shares for pre-funded warrants to purchase Company Series E Preferred Shares (the “Exchange Transaction”);

WHEREAS, pursuant to Section 8.3 of the Business Combination Agreement, the Business Combination Agreement may be amended, modified or supplemented by an agreement in writing executed by ARYA and the Company; and

WHEREAS, ARYA and the Company hereby desire to enter into this Consent and Amendment in accordance with the terms below.

NOW, THEREFORE for good and valuable consideration, the receipt and sufficiency of which are hereby acknowledged, the Parties hereby agree as follows:

1. Definitions. Capitalized terms used in this Consent and Amendment and not otherwise defined herein shall have the respective meanings ascribed to them in the Business Combination Agreement.

2. Amendments. The Business Combination Agreement is hereby amended as follows:

The definition of “Fully-Diluted Company Capitalization” is hereby deleted in its entirety and replaced with the following:

“Fully-Diluted Company Capitalization” means, without duplication, the sum of (a) the aggregate number of Company Shares outstanding as of immediately prior to the Company Merger Effective Time (and after, for the avoidance of doubt, giving effect to (i) the Company Preferred Shares Conversion, (ii) the termination or net exercise of the Company Warrants pursuant to Section 2.4(e), and (iii) the Company Convertible Notes Conversion), (b) the aggregate number of Company Shares underlying the Pre-Funded Company Warrants and (c) the aggregate number of Company Shares subject to In-the-Money Options as of immediately prior to the Company Merger Effective Time.

The definition of “Company Warrants” is hereby deleted in its entirety and replaced with the following:

“Company Warrants” means, as of any determination time, each warrant (or similar instrument) to purchase Company Shares that is outstanding, including those listed on Section 2.4(d) of the Company Disclosure Schedules. Notwithstanding the foregoing, and for the avoidance of doubt, Company Warrants shall not include the Pre-Funded Company Warrants.

Section 2.1(d)(vii) of the Business Combination Agreement is hereby deleted in its entirety and replaced with the following:

(vii) At the Company Merger Effective Time, by virtue of the Company Merger and without any action on the part of any Party or any other Person, (A) each Company Share (other than any Dissenting Company Shares and the Company Shares cancelled and extinguished pursuant to Section 2.1(d)(viii)) and (B) each Pre-Funded Company Warrant issued and outstanding as of immediately prior to the Company Merger Effective Time shall be automatically canceled and extinguished and converted into the right to receive a number of Holdco Shares equal to the Exchange Ratio. From and after the Company Merger Effective Time, except as otherwise expressly provided for herein or under applicable Law, (x) each Company Shareholder’s Certificates, if any, evidencing ownership of the Company Shares and the Company Shares held in book-entry form issued and outstanding immediately prior to the Company Merger Effective Time shall each cease to have any rights with respect to such Company Shares and (y) each Pre-Funded Company Warrant issued and outstanding immediately prior to the Company Merger Effective Time shall be terminated and each holder thereof shall cease to have any rights with respect thereto.

Section 2.3(a) of the Business Combination Agreement is hereby deleted in its entirety and replaced with the following:

(a) At least three (3) Business Days prior to the Closing Date, the Company shall deliver to ARYA and HoldCo an allocation schedule (the “Allocation Schedule”) (x) setting forth: (i) (A) the number and type of Company Shares held by each Company Shareholder and the number of Company Common Shares that will be held by each such Company Shareholder after giving effect to the conversion of the Company Preferred Shares pursuant to Section 2.4(b), (B) the number and type of Company Shares subject to each Company Warrant held by each holder thereof and the number and type of Company Shares that will be held by each such holder after giving effect to the exercise or termination of Company Warrants pursuant to Section 2.4(e), (C) the number and type of Company Shares subject to each Company Option held by each holder thereof that is outstanding and whether such Company Option will be an In-the-Money Option as of immediately prior to the Company Merger Effective Time, (D) the number and type of Company Shares that will be held by each holder of Company Convertible Notes after giving effect to the Company Convertible Notes Conversion pursuant to Section 2.4(a), (E) the number and type of Company Shares subject to each Pre-Funded Company Warrant held by each holder thereof, as well as, in each case, reasonably detailed calculations with respect to the components and subcomponents thereof (including any conversion, exchange (or similar) ratio on which such calculations are based); (ii) in the case of the Company Options, the Company Warrants, and the Pre-Funded Company Warrants, the exercise (or similar) price and, if applicable, the exercise (or similar) date; and (iii) (A) the Adjusted Equity Value, the Adjusted Transaction Share Consideration, the Fully-Diluted Company Capitalization and the Exchange Ratio, as well as, in each case, reasonably detailed calculations of the components and subcomponents thereof, (B) the portion of the Adjusted Transaction Share Consideration allocated to each In-the-Money Option pursuant to Section 2.4(c) and the exercise price of each Rollover In-the-Money Option at the Company Merger Effective Time determined pursuant to Section 2.4(c), as well as, in each case, reasonably detailed calculations of the components and subcomponents thereof, and (C) the portion of the Adjusted Transaction Share Consideration allocated to each holder of Company Common Shares pursuant to Section 2.1(d)(vii) (including, for the avoidance of doubt, each Company Common Share that is issued in connection with the Company Preferred Shares Conversion, the Company Warrant Exercise and the Company Convertible Notes Conversion), as well as, in each case, reasonably detailed calculations with respect to the components and subcomponents thereof; and that includes (y) a certification duly executed by an authorized officer of the Company, in his or her capacity as an officer of the Company and not in his or her individual capacity, that the information and calculations delivered pursuant to this Section 2.3(a) are, and will be as of immediately prior to the Company Merger Effective Time, (i) true and correct in all respects (other than de minimis inaccuracies of which the Company does not have knowledge), and (ii) in accordance with the Allocation Schedule Requirements.

The definition of “Fully-Diluted HoldCo Closing Capitalization” is hereby deleted in its entirety and replaced with the following:

““Fully-Diluted HoldCo Closing Capitalization” means, without duplication, the sum of (a) the number of HoldCo Shares outstanding immediately after the Company Merger Effective Time, (b) the number of HoldCo Shares that are subject to Rollover In-the-Money Options and deemed to be outstanding based on the application of the treasury share method, (c) the Earn-Out Shares (as defined in the Sponsor Letter Agreement), and (d) the number of pre-funded warrants outstanding immediately after the Company Merger Effective Time that each represent the right to purchase HoldCo Shares. Notwithstanding the foregoing, and for the avoidance of doubt, Fully-Diluted HoldCo Closing Capitalization shall not include (x) the number of HoldCo Warrants issuable pursuant to the PIPE Subscrption Agreements (other than the pre-funded warrants described in subclause (d) above), (y) HoldCo Shares issuable pursuant to the HoldCo Convertible Notes and (z) HoldCo Warrants issuable pursuant to the Convertible Security Subscription Agreements.

The following definitions are hereby added to Section 1.1 of the Business Combination Agreement.

“Aggregate HoldCo Share Reserve” means the aggregate number of HoldCo Shares equal to the quotient obtained by dividing (i) the Fully Diluted HoldCo Closing Capitalization by (ii) sixty-five percent (65%).

“Aggregate Incentive Equity Pool” means the aggregate number of HoldCo Shares equal to (i) the Aggregate HoldCo Share Reserve minus (ii) the Fully Diluted HoldCo Closing Capitalization.

“Incentive Equity Plan Maximum Amount” means the aggregate number of HoldCo Shares equal to the product obtained by multiplying (i) the quotient of (x) twenty percent (20%) divided by (y) thirty-five percent (35%) by (ii) the Aggregate Incentive Equity Pool.

“Key Employee Incentive Plan Maximum Amount” means the aggregate number of HoldCo Shares equal to the product obtained by multiplying (i) the quotient of (x) fifteen percent (15%) divided by (y) thirty-five percent (35%) by (ii) the Aggregate Incentive Equity Pool.

“Pre-Funded Company Warrants” means, as of any determination time, each outstanding pre-funded warrant (or similar instrument) of the Company that represents the right to purchase Company Series E Preferred Shares.

Section 5.20 of the Business Combination Agreement is hereby deleted in its entirety and replaced with the following:

Section 5.20 Key Employee Equity Awards. Prior to the effectiveness of the Registration Statement / Proxy Statement, the HoldCo Board shall approve and adopt an equity incentive plan in a form to be mutually agreed between ARYA and the Company (such agreement not to be unreasonably withheld, conditioned or delayed) (the “Key Employee Incentive Plan”), which shall provide for an aggregate share reserve thereunder of up to the Key Employee Incentive Plan Maximum Amount, for purposes of making grants of awards to mutually agreed key employees of the Company at the Closing. Awards granted pursuant to the Key Employee Incentive Plan shall be made in a form and manner, and upon such terms and conditions, as are mutually agreed between ARYA and the Company (such agreement not to be unreasonably withheld, conditioned or delayed by either ARYA or the Company) prior to the Closing. Notwithstanding the foregoing, the Key Employee Incentive Plan will allow HoldCo to reprice awards granted thereunder without the approval of the stockholders of HoldCo.

Section 5.21 of the Business Combination Agreement is hereby deleted in its entirety and replaced with the following:

Section 5.21 Post-Closing HoldCo Incentive Equity Plan. Prior to the effectiveness of the Registration Statement / Proxy Statement, the HoldCo Board shall approve and adopt an equity incentive plan in a form to be mutually agreed between ARYA and the Company (such agreement not to be unreasonably withheld, conditioned or delayed) (the “HoldCo Incentive Equity Plan”), effective as of one (1) day prior to the Closing Date, which shall provide for an aggregate share reserve thereunder equal to the Incentive Equity Plan Maximum Amount, plus an increase commencing on January 1, 2025 and continuing annually on the anniversary thereof through (and including) January 1, 2034, equal to the lesser of (a) five percent (5%) of the number of HoldCo Shares outstanding on the last day of the immediately preceding calendar year and (b) such smaller number of HoldCo Shares as determined by the HoldCo Board or the compensation committee of the HoldCo Board. Notwithstanding the foregoing, the HoldCo Incentive Equity Plan will allow HoldCo to reprice the awards granted thereunder without the approval of the stockholders of HoldCo.

The second sentence of Section 2.1(b) of the Business Combination Agreement is hereby deleted in its entirety and replaced with the following:

Following the Closing, HoldCo’s name will be changed to “Adiago Medical Holdings, Inc.”, provided that if such name is not available in Delaware or HoldCo is otherwise unable to change its name to “Adiago Medical Holdings, Inc.” in Delaware, it shall cause its name to be changed to such other name mutually agreed to by ARYA and the Company (such agreement not to be unreasonably withheld, conditioned or delayed).

j.	Section 5.28 of the Business Combination Agreement is hereby deleted in its entirety and replaced with “[Intentionally Omitted]”.

3. Consent. ARYA hereby consents to the Company entering into the Exchange Agreement, the other documents necessary to effectuate the Exchange Transaction and the transactions contemplated thereby, including the Exchange Transaction, and agrees that such consent shall be deemed to fully satisfy any and all requirements that may be applicable under the Business Combination Agreement regarding the requirement for obtaining ARYA’s consent thereto.

4. Effect of this Consent and Amendment. Except as expressly provided by this Consent and Amendment, each of the provisions of the Business Combination Agreement shall remain unchanged and in full force and effect following the execution of this Consent and Amendment. Following the execution of this Consent and Amendment, references in the Business Combination Agreement to “this Agreement”, “herein”, “hereof” or phrases having a similar meaning shall refer to the Business Combination Agreement as amended by this Consent and Amendment.

5. Entire Agreement. This Consent and Amendment and the Business Combination Agreement constitute the entire agreement among the Parties with respect to the subject matter hereof and supersedes all other prior agreements and understandings, both written and oral, among the Parties or any of their respective Subsidiaries with respect to the subject matter hereof.

6. General Provisions. Section 8.4 (Notices), Section 8.5 (Governing Law), Section 8.7 (Construction; Interpretation), Section 8.10 (Severability), Section 8.11 (Counterparts; Electronic Signatures), Section 8.15 (Waiver of Jury Trial) and Section 8.16 (Submission to Jurisdiction) of the Business Combination Agreement are incorporated herein by reference and shall apply, mutatis mutandis, to this Consent and Amendment as though fully set forth herein.

[Signature pages follow]

IN WITNESS WHEREOF, the Parties hereto have caused this Consent and Amendment to be executed by their respective authorized representatives as of the date first written above.

	ARYA SCIENCES ACQUISITION CORP IV

	By:	/s/ Michael Altman
	Name:	Michael Altman
	Title:	Chief Financial Officer


	ADAGIO MEDICAL, INC.

	By:	/s/ John Dahldorf
	Name:	John Dahldorf
	Title:	Chief Financial Officer

[Signature Page to Consent and Amendment No. 1 to Business Combination Agreement]