Exhibit 5.1

August 13, 2025

Compass Therapeutics, Inc.

80 Guest Street

Suite 601

Boston, Massachusetts 02135

Re: Securities Registered under Registration Statement on Form S-3

We have acted as counsel to you in connection with your filing of a Registration Statement on Form S-3 (File No. 333-281891) (as amended or supplemented, the “Registration Statement”) filed on August 30, 2024 with the Securities and Exchange Commission (the “Commission”) pursuant to the Securities Act of 1933, as amended (the “Securities Act”), relating to the registration of the offer by Compass Therapeutics, Inc., a Delaware corporation (the “Company”), of up to $300,000,000 of any combination of securities of the types specified therein. The Registration Statement was declared effective by the Commission on September 6, 2024. Reference is made to our opinion letter dated August 30, 2024 and included as Exhibit 5.1 to the Registration Statement. We are delivering this supplemental opinion letter in connection with the prospectus supplement (the “Prospectus Supplement”) filed on August 13, 2025 by the Company with the Commission pursuant to Rule 424 under the Securities Act. The Prospectus Supplement relates to the offering by the Company of (i) up to 33,290,000 shares (the “Shares”) of the Company’s common stock, par value $0.0001 per share (the “Common Stock”), and (ii) pre-funded warrants to purchase up to 6,710,000 shares (the “Pre-Funded Warrant Shares”) of Common Stock of the Company (the “Pre-Funded Warrants”), covered by the Registration Statement. The Shares include an over-allotment option granted to the underwriters of the offering to purchase 6,000,000 shares of Common Stock. The Shares and Pre-Funded Warrants are being sold to the several underwriters named in, and pursuant to, an underwriting agreement among the Company and such underwriters (the “Underwriting Agreement”).

We have reviewed such documents and made such examination of law as we have deemed appropriate to give the opinion set forth below. We have relied, without independent verification, on certificates of public officials and, as to matters of fact material to the opinion set forth below, on certificates of officers of the Company.

The opinions set forth below are limited to the Delaware General Corporation Law and, with regard to numbered paragraph 2 below, the law of New York.

Based on the foregoing, we are of the opinion that

Compass Therapeutics, Inc.

August 12, 2025

Page 2

1. The Shares have been duly authorized and, when delivered and paid for in accordance with the terms of the Underwriting Agreement, will be validly issued, fully paid and non-assessable.

2. The Pre-Funded Warrants have been duly authorized by the Company and, when executed by the Company and delivered and paid for in accordance with the terms of the Underwriting Agreement, will be valid and binding obligations of the Company.

3. Assuming the Pre-Funded Warrant Shares were issued today in accordance with the terms of the Pre-Funded Warrants, they will be validly issued, fully paid and non-assessable.

Our opinions expressed above are subject to bankruptcy, insolvency, fraudulent transfer, reorganization, moratorium and other similar laws of general application affecting the rights and remedies of creditors and to general principles of equity.

This opinion letter and the opinions it contains shall be interpreted in accordance with the Core Opinion Principles as published in 74 Business Lawyer 815 (Summer 2019).

We hereby consent to the inclusion of this opinion as Exhibit 5.1 to the Company’s Current Report on Form 8-K to be incorporated by reference into the Registration Statement and to the references to our firm under the caption “Legal Matters” in the Registration Statement. In giving our consent, we do not admit that we are in the category of persons whose consent is required under Section 7 of the Securities Act or the rules and regulations thereunder.

Very truly yours,

/s/ GOODWIN PROCTER LLP

GOODWIN PROCTER LLP