Amendment to the November 14, 2017 Second Amended and Restated Rights Agreement as of November 9, 2022, by and between AIM ImmunoTech Inc. (f/k/a Hemispherx Biopharma, Inc.) and American Stock Transfer & Trust Company, LLC

Exhibit 4.1

AMENDMENT

TO THE

SECOND AMENDED AND RESTATED RIGHTS AGREEMENT

OF

AIM IMMUNOTECH INC.

This Amendment to the Second Amended and Restated Rights Agreement (this “Amendment”) is made this 9^th day of November, 2022, by and between AIM ImmunoTech Inc., f/k/a Hemispherx Biopharma, Inc., a Delaware corporation (the “Company’), and American Stock Transfer & Trust Company, LLC, a New York limited liability trust company (the “Rights Agent”).

WHEREAS, on November 19, 2002, the Company entered into the original Rights Agreement (the “Original Agreement”) with Continental Stock Transfer & Trust Company (“CST”) as the rights agent;

WHEREAS, the Company and CST amended and restated the Original Agreement on November 2, 2012 (the “2012 Agreement”);

WHEREAS, on April 26, 2017, the Company terminated CST as the rights agent under the Amended Agreement and appointed AST as the Rights Agent and AST accepted the appointment;

WHEREAS, the Company and the Rights Agent further amended and restated the 2012 Agreement on November 14, 2017 (as so amended and restated, the “Rights Agreement”);

WHEREAS, the Board of Directors of the Company (the “Board”) has determined that it is advisable and in the best interests of the Company and its stockholders to amend the Rights Agreement in accordance with Section 27 thereof; and

WHEREAS, pursuant to its authority under Section 27 of the Rights Agreement, the Board has approved, and directed that the Rights Agent approve, this Amendment.

NOW, THEREFORE, in consideration of the premises and mutual covenants contained in this Amendment, and other good and valuable consideration, the receipt and sufficiency of which are hereby acknowledged, the Company and the Rights Agent hereby agree as follows:

1. Definitions. Capitalized terms used but not defined in this Amendment shall have the meanings given to them in the Rights Agreement.

2. Amendment. Section 7(a) of the Rights Agreement is hereby amended and restated in its entirety to read as follows:

(a) Subject to Section 7(e) hereof, at any time after the Distribution Date the registered holder of any Rights Certificate may exercise the Rights evidenced thereby (except as otherwise provided herein, including, without limitation, the restrictions on exercisability set forth in Section 9(c), Section 11(a)(iii) and Section 23(a) hereof) in whole or in part upon surrender of the Rights Certificate, with the form of election to purchase and the certificate on the reverse side thereof duly executed, to the Rights Agent at the principal office or offices of the Rights Agent designated for such purpose, together with payment of the aggregate Purchase Price with respect to the total number of one one-hundredths of a share (or other securities, cash or other assets, as the case may be) as to which such surrendered Rights are then exercisable, at or prior to the earlier of (i) 5:00 P.M., New York City time, on February 14, 2023 (or such later date as may be established by the Board of Directors prior to the expiration of the Rights) (such date the “Final Expiration Date”), or (ii) the time at which the Rights are redeemed or exchanged as provided in Section 23 and Section 24 hereof (the earlier of (i) and (ii) being herein referred to as the “Expiration Date”).

3. Other Terms. Except as set forth in this Amendment, (i) all provisions of the Rights Agreement shall remain unmodified and in full force and effect and (ii) nothing contained in this Amendment shall amend, modify or otherwise affect the Rights Agreement or any party’s rights or obligations contained therein.

4. Counterparts. This Amendment may be executed in any one or more counterparts, each of which shall be deemed an original and all of which shall together constitute the same instrument.

[Signature page follows.]

IN WITNESS WHEREOF, the parties have executed and delivered this Amendment as of the date first above written.