Exhibit 99.E

October 12, 2023

American Oncology Network, Inc.

14543 Global Parkway, Suite 110

Fort Myers, FL 33913

Ladies and Gentlemen:

In addition to any shares of Class A Common Stock, par value $0.0001 per share (the “Class A Common Stock”), of American Oncology Network, Inc. (the “Company”) the undersigned may hold, the undersigned holds shares of Series A Preferred Stock, par value $0.0001 per share (the “Series A Preferred Stock” and, together with any other securities acquired by the undersigned on or after the date hereof which are exercisable for, convertible into or otherwise exchangeable for Class A Common Stock, including but not limited to shares of Class B Common Stock, par value $0.0001 per share, of the Company or units of American Oncology Network, LLC, a wholly-owned subsidiary of the Company, “Equity-Linked Securities”), of the Company, which have not been and are not expected to be registered under the Securities and Exchange Act of 1934, as amended (the “Exchange Act”). Each of the Class A Common Stock and the Company’s Warrants, each whole warrant exercisable for one share of Class A Common Stock, are registered pursuant to Section 12(b) of the Exchange Act.

Pursuant to the Company’s Amended and Restated Certificate of Incorporation and Certificate of Designations, each as filed with the Secretary of State of the State of Delaware on September 20, 2023 (collectively the “Charter”), each share of Series A Preferred Stock will be converted into that number of shares of Class A Common Stock equal to the conversion ratio then in effect, with such adjustment or cash payment for fractional shares as the Company may elect pursuant to the Charter, either (a) at the option of the Company on or after September 20, 2026 (subject to certain restrictions set forth in the Certificate of Designations) or (b) at the option of the holder.

Certain stockholders of the Company are required to make filings with the Securities and Exchange Commission (the “SEC”) under Sections 13 and 16 of the Exchange Act. Filings pursuant to Sections 13 and 16 of the Exchange Act are typically required of stockholders who beneficially own (as defined in Rule 13d-3 of the Exchange Act) more than five percent or ten percent, respectively, of the outstanding shares of a class of a company’s equity securities registered under the Exchange Act (with respect to Section 13 of the Exchange Act, the Class A Common Stock).

In consideration of the foregoing, the undersigned agrees that it will not convert its Equity-Linked Securities, whether beneficially owned as of the date hereof or hereafter acquired, into shares of Class A Common Stock to the extent that such conversion would result in the undersigned, together with any Attribution Parties (as defined below), beneficially owning more than 4.99% of the outstanding shares of Class A Common Stock; provided that the foregoing limitation may be waived by the undersigned by giving at least sixty-one (61) days prior notice to the Company (the “Conversion Notice”). “Attribution Parties” shall mean: (i) any direct or indirect affiliates of the undersigned; (ii) any person acting or who could be deemed to be acting as a group (as that term is used in Section 13(d) of the Exchange Act and as defined in Rule 13d- 5 thereunder) together with the undersigned; and (iii) any persons whose beneficial ownership of Class A Common Stock would or could be aggregated with the undersigned’s and the other Attribution Parties’ for purposes of Section 13 and/or Section 16 of the Exchange Act.

The limitations set forth in the prior paragraph will terminate upon the sixty-first (61st) day after a Conversion Notice is delivered to the Company. The undersigned understands that, after the Conversion Notice is delivered to the Company, it will be required to make filings with the SEC under Sections 13 and 16 of the Exchange Act if the conversion of Equity-Linked Securities beneficially owned by the undersigned will result in the undersigned, together with any Attribution Parties, collectively beneficially owning more than five percent or ten percent, respectively, of the outstanding shares of Class A Common Stock. The undersigned also understands that the Company will instruct its transfer agent to restrict the undersigned’s Equity-Linked Securities in accordance with this Conversion Restriction Agreement.

For the avoidance of doubt, this Conversion Restriction Agreement shall not have, and is not intended to have, the purpose or effect of altering or otherwise affecting the determination of voting rights or voting power of the Series A Preferred Stock as set forth in Section 4(a) of the Certificate of Designations.

Notwithstanding the foregoing, this Conversion Restriction Agreement shall automatically expire on the earlier of (i) the date on which the undersigned, together with any Attribution Parties, collectively beneficially owns less than five percent of the outstanding shares of Class A Common Stock, assuming conversion of all Equity-Linked Securities held by the undersigned and any such Attribution Parties, or (ii) the consummation of a change in control of the Company.

Other than as expressly set forth herein, this Conversion Restriction Agreement is irrevocable and will be binding upon the undersigned’s heirs, legal representatives, successors and assigns. This Conversion Restriction Agreement may be executed in any number of counterparts, each of which constitutes an original, and all of which taken together constitute one agreement binding on all the parties.

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Very truly yours,
AEA GROWTH EQUITY FUND LP
By: AEA Growth Equity Partners LP
Its general partner
By: AEA Growth Equity GP LLC
Its general partner
By:	/s/ Michelle Marcellus
Name:	Michelle Marcellus
Title:	Vice President
AEA GROWTH EQUITY FUND (PARALLEL) LP
By: AEA Growth Equity Partners LP
Its general partner
By: AEA Growth Equity GP LLC
Its general partner
By:	/s/ Michelle Marcellus
Name:	Michelle Marcellus
Title:	Vice President
AEA GROWTH EQUITY PARTNERS LP
By: AEA Growth Equity GP LLC
Its general partner
By:	/s/ Michelle Marcellus
Name:	Michelle Marcellus
Title:	Vice President
AEA GROWTH EQUITY GP LLC
By:	/s/ Barbara L. Burns
Name:	Barbara L. Burns
Title:	Vice President
AEA Management UGP LLC
By:	/s/ Barbara L. Burns
	Name: Barbara L. Burns
	Its: Vice President
BRIAN R. HOESTEREY
By:	/s/ Barbara L. Burns
Barbara L. Burns, Attorney-in-Fact

Agreed and acknowledged:
AMERICAN ONCOLOGY NETWORK, INC.
By:	/s/ Todd Schonherz
Name:	Todd Schonherz
Title:	Chief Executive Officer