Exhibit 3.1

FIRST AMENDMENT TO

EQUITY DISTRIBUTION AGREEMENT

This FIRST AMENDMENT TO EQUITY DISTRIBUTION AGREEMENT (this “Amendment”) is entered into as of April 10, 2026, by and between AIM ImmunoTech Inc., a Delaware corporation (the “Company”), and Maxim Group LLC (the “Agent”).

WHEREAS, the Company and the Agent entered into an Equity Distribution Agreement, dated April 1, 2025 (the “Agreement”), pursuant to which the Company may issue and sell, through the Agent, its shares of common stock;

WHEREAS, the Agreement provides that the Company may cause the Agent to sell common stock of the Company having an aggregate offering price of up to $3.0 million; and

WHEREAS, the Company and the Agent wish to amend the title, introductory paragraph and Sections 2(a), 3(q), 7(a) and 9 of the Agreement to remove the limit on the number of shares of the Company’s common stock that may be sold pursuant to the Agreement and to make necessary updates to references throughout the Agreement to the Company’s legal counsel.

NOW, THEREFORE, in consideration of the mutual agreements contained herein and other good and valuable consideration, the receipt and sufficiency of which are hereby acknowledged, and intending to be legally bound hereby, the Company and the Agent hereby agree as follows:

1. Title of the Agreement. The title of the Agreement is hereby amended and restated in its entirety as follows:

AIM ImmunoTech Inc.

Equity Distribution Agreement

2. Amendment to the Introductory Paragraph of the Agreement. The introductory paragraph of the Agreement is hereby amended and restated in its entirety as follows:

“AIM ImmunoTech Inc., a Delaware corporation (the “Company”), proposes to issue and sell through Maxim Group LLC (the “Agent”), as sales agent, shares of common stock, par value $0.001 per share (“Common Stock”), of the Company (the “Shares”) on terms set forth herein. The Shares consist entirely of authorized but unissued shares of Common Stock to be issued and sold by the Company.”

3. Amendment to “Purchase, Sale and Delivery of Shares.” Sections 2(a) and 2(a)(i) of the Agreement is hereby amended and restated in its entirety as follows:

(a) At the Market Sales. On the basis of the representations, warranties and agreements herein the Company agrees that, from time to time after the effective date of the Registration Statement on the terms and subject to the conditions set forth herein, it may issue and sell through the Agent, acting as sales agent, Shares; provided, however, that in no event shall the Company issue or sell through the Agent such number of Shares that (a) exceeds the number or dollar amount of shares of Common Stock registered on the Registration Statement pursuant to which the Offering is being made, (b) exceeds the number of authorized but unissued shares of Common Stock under the Company’s Amended and Restated Certificate of Incorporation, as amended or (c) would cause the Company or the Offering to not satisfy the eligibility and transaction requirements for use of Form S-3 (including, if then applicable, General Instruction I.B.6 of Form S-3) (the lesser of (a), (b) and (c), the “Maximum Amount”). Notwithstanding anything to the contrary contained herein, the parties hereto agree that compliance with the limitations set forth in this Section 2(a) on the number and aggregate sales price of Shares issued and sold under this Agreement shall be the sole responsibility of the Company and the Agent shall have no obligation in connection with such compliance. Notwithstanding the foregoing, the Company agrees that it will provide the Agent with written notice of the Maximum Amount available for sale of the Shares no less than one (1) Business Day prior to the date on which it makes the initial sale of Shares under this Agreement. “Business Day”, as used herein, shall mean any day other than Saturday, Sunday or other day on which commercial banks in The City of New York are authorized or required by law to remain closed; provided that banks shall not be deemed to be authorized or obligated to be closed due to a “shelter in place,” “non-essential employee” or similar closure of physical branch locations at the direction of any governmental authority if such banks’ electronic funds transfer systems (including for wire transfers) are open for use by customers on such day.

(i) For purposes of selling the Shares through the Agent, the Company hereby appoints the Agent as agent of the Company for the purpose of soliciting purchases of the Shares from the Company pursuant to this Agreement and the Agent agrees to use its commercially reasonable efforts to sell the Shares on the terms and subject to the conditions stated herein.

4. Amendment to “Covenant.” Section 3(q) of the Agreement is hereby amended restated in its entirety as follows:

(q) (1) On the date hereof, the Company shall cause (A) Thompson Hine LLP, counsel for the Company, to furnish to the Agent its written opinion and negative assurance letter, in form and substance reasonably acceptable to Agent’s counsel and (B) Studebaker & Brackett PC, intellectual property legal counsel to the Company, to furnish to the Agent its written opinion, in form and substance reasonably acceptable to Agent’s counsel, and the Agent shall cause (C) Ellenoff Grossman & Schole LLP, as counsel for the Agent to furnish to the Agent its negative assurance letter.

(2) On each date that the Company (i) amends or supplements the Registration Statement after the effective date of the Registration Statement or the Prospectus (other than by means of incorporation by reference); (ii) files an annual report on Form 10-K under the Exchange Act; (iii) files its quarterly reports on Form 10-Q under the Exchange Act; (iv) files a report on Form 8-K under the Exchange Act containing amended financial information (other than an earnings release, to “furnish” information pursuant to Items 2.02 or 7.01 of Form 8-K, unless the Agent reasonably determines that the information in such Form 8-K is material); or (v) otherwise after each reasonable request by Agent (each of such date referred to herein as a “Bringdown Date”), the Company shall cause (X) Thompson Hine LLP, counsel for the Company, to furnish to the Agent its opinion and negative assurance letter, in form and substance reasonably acceptable to Agent’s counsel, and (Y) Studebaker & Brackett PC, intellectual property legal counsel to the Company, to furnish to the Agent its written opinion, in form and substance reasonably acceptable to Agent’s counsel, and the Agent shall cause (Z) Ellenoff Grossman & Schole LLP, as counsel for the Agent to furnish to the Agent its negative assurance letter, each dated as of a date within ten (10) days after the applicable Bringdown Date, addressed to the Agent and modified as necessary to relate to the Registration Statement and the Prospectus as amended and supplemented to the time of delivery of such opinions. With respect to this Section 3(q)(2), in lieu of delivering such opinions or letters for Bringdown Dates subsequent to the date of effectiveness of the Registration Statement, such counsel may furnish agent with a letter (a “Reliance Letter”) to the effect that Agent may rely upon a prior opinion or letter delivered under Section 3(q)(1) or this Section 3(q)(2) to the same extent as if it were dated the date of such letter (except that statements in such prior opinion shall be deemed to relate to the Registration Statement and the Prospectus as amended or supplemented as of the date of Reliance Letter). Provided, however, the requirement to provide opinions and letters under this Section 3(q)(2) is hereby waived for any Bringdown Date occurring at a time at which no Transaction Notice is pending, which waiver shall continue until the earlier to occur of the date the Company delivers a Transaction Notice hereunder and the next occurring Bringdown Date. Notwithstanding the foregoing, if the Company subsequently decides to sell Shares following a Bringdown Date when the Company relied on such waiver and did not provide Agent with opinions and letters under this Section 3(q)(2), then before the Company delivers the Transaction Notice or Agent sells any Shares, the Company shall cause each of Thompson Hine LLP to furnish to the Agent a written opinion and negative assurance letter, and Studebaker & Brackett PC to furnish to the agent its written opinion, and the Agent shall cause Ellenoff Grossman & Schole LLP to furnish to the Agent its negative assurance letter, dated the date of the Transaction Notice.

5. Amendment to “Termination of this Agreement.” Section 7 of the Agreement is hereby amended and restated in its entirety as follows:

“7. Termination of this Agreement. The term of this Agreement shall begin on the date hereof, and shall continue until termination by either the Agent and the Company upon the provision of fifteen (15) days written notice. Any such termination by mutual agreement shall in all cases be deemed to provide that Section 3(g), Section 5 and Section 6 shall remain in full force and effect. Notwithstanding the foregoing, the Agent shall have the right, in its sole discretion, to terminate this Agreement if at any time from the date of this Agreement to the effectiveness of the Registration Statement, the Agent is not fully satisfied, in its sole discretion, with the results of its and its representatives’ review of the Company and the Company’s business.”

6. Amendment to “Notice.” Section 9 of the Agreement is hereby amended and restated in its entirety as follows:

“9. Notices. Except as otherwise provided herein, all communications under this Agreement shall be in writing and, if to the Agent, shall be mailed, delivered or telecopied to Maxim Group LLC, 300 Park Avenue, 16th Floor, New York, New York 10022, Attention: Clifford A. Teller and James Siegel, with a required copy (which shall not constitute notice) to Ellenoff Grossman & Schole LLP, counsel for the Agent, at 1345 Avenue of the Americas, New York, New York 10105 Attention: Matt Bernstein, Esq. Notices to the Company shall be given to it at 2117 SW Highway 484, Ocala FL 34473 Attention: Chief Executive Officer, with required copies (which shall not constitute notice) to Thompson Hine LLP, 300 Madison Avenue, 27th Floor, New York, New York 10017, Attention: Faith L. Charles. Any party to this Agreement may change such address for notices by sending to the parties to this Agreement written notice of a new address for such purpose.”

7. No Further Amendment. Except as amended by this Amendment, the Agreement remains unaltered and shall remain in full force and effect.

8. Jurisdiction. All questions concerning the construction, validity, enforcement and interpretation of this Amendment shall be determined in accordance with the provisions of the Agreement.

9. Counterparts. This Amendment may be executed in any number of counterparts, each of which will be deemed an original and all of which together will constitute one and the same instrument. Signatures delivered by facsimile, electronic mail (including as a PDF file) or other transmission method shall be deemed to be original signatures, shall be valid and binding, and, upon delivery, shall constitute due execution of this Amendment.

[Signature page follows]
 

IN WITNESS WHEREOF, each of the Company and the Agent has caused this Amendment to be executed and delivered by its officer thereunto duly authorized as of the date first above indicated.

Exhibit 5.1

April 10, 2026

AIM ImmunoTech Inc.

2117 SW Highway 484

Ocala, FL 34473

Re: AIM ImmunoTech Inc. Common Stock

Ladies and Gentlemen:

We have acted as counsel to AIM ImmunoTech Inc., a Delaware corporation (the “Company”), with respect to certain matters in connection with the offering by the Company of $3,409,174 of shares of the Company’s common stock, par value $0.001 per share (the “Shares”), pursuant to the Registration Statement on Form S-3 (File No. 333-286319) (the “Registration Statement”), filed with the Securities and Exchange Commission (the “Commission”) under the Securities Act of 1933, as amended (the “Act”), the related prospectus dated July 3, 2025 included within the Registration Statement (the “Base Prospectus”), the prospectus supplement dated October 30, 2025, and the amendment to the prospectus supplement dated April 10, 2026, filed with the Commission pursuant to Rule 424(b) promulgated under the Act (together with the Base Prospectus, the “Prospectus”). The Shares are to be sold by the Company in accordance with the Equity Distribution Agreement dated April 1, 2025, as amended on April 10, 2026, by and between the Company and Maxim Group LLC (the “EDA”), as described in the Prospectus.

In rendering this opinion, we have examined and are familiar with the following:

In such examination, we have assumed:

AIM ImmunoTech Inc.

April 10, 2026

Page 2

Based upon and subject to the foregoing and such other investigation as we have deemed necessary and subject to the qualifications set forth below, we are of the opinion that the Shares, when issued by the Company out of the Company’s duly authorized common stock and issued and delivered by the Company against payment therefor as contemplated by and in accordance with the terms of the EDA, on terms approved by the Board of Directors of the Company, or a duly authorized committee thereof, will be duly and validly issued, fully paid and nonassessable.

Our opinions expressed above are limited to the General Corporation Laws of the State of Delaware and laws of the State of New York, in each case as currently in effect (collectively, “Applicable Law”), and we express no opinion as to the effect on the matters covered by this letter of the laws of any other jurisdiction.

We have relied as to certain matters on information obtained from public officials, officers of the Company, and other sources believed by us to be responsible.

Please note that we are opining only as to the matters expressly set forth herein, and no opinion should be inferred as to any other matters. This opinion is based upon currently existing statutes, rules, regulations and judicial decisions, and we disclaim any obligation to advise you of any change in any of these sources of law or subsequent legal or factual developments which might affect any matters or opinions set forth herein.

We hereby consent to the filing of this opinion as an exhibit to a Current Report on Form 8-K in accordance with the requirements of Item 601(b)(5) of Regulation S-K under the Act. In giving such consent, we do not hereby admit that we are in the category of persons whose consent is required under Section 7 of the Act or the rules and regulations of the Commission.

Very truly yours,

/s/ Thompson Hine LLP

Thompson Hine LLP