VIA EDGAR

September 23, 2020

United States Securities and Exchange Commission

Division of Corporation Finance

Office of Life Sciences

Mail Stop 4561

100 F Street, N.E.

Washington, D.C. 20549

Attention: Margaret Schwartz

Re: Compass Therapeutics, Inc.

Acceleration Request for Registration Statement on Form S-1

File No. 333-244353

Dear Ms. Schwartz:

Pursuant to Rule 461 under the Securities Act of 1933, as amended (the “Act”), Compass Therapeutics, Inc. (the “Company”) hereby requests that the effective date of the above-referenced registration statement (the “Registration Statement”) be accelerated to September 25, 2020, at 4:00 p.m., Eastern Time, or as soon thereafter as practicable, unless we or our outside counsel, Goodwin Procter LLP, request by telephone that such Registration Statement be declared effective at some other time. In making this acceleration request, the Company acknowledges that it is aware of its responsibilities under the Act.

Once the Registration Statement is effective, please orally confirm the event with our counsel, Goodwin Procter LLP by calling James Xu at (617) 570-1483. We also respectfully request that a copy of the written order from the Securities and Exchange Commission (the “Commission”) verifying the effective time and date of the Registration Statement be sent to our counsel, Goodwin Procter LLP, Attention: James Xu, by email at JXu@goodwinlaw.com.

If you have any questions regarding this request, please contact James Xu of Goodwin Procter LLP at (617) 570-1483.