September 3, 2024

Thomas Schuetz
Chief Executive Officer
Compass Therapeutics, Inc.
80 Guest Street
Suite 601
Boston, Massachusetts 02135

       Re: Compass Therapeutics, Inc.
           Registration Statement on Form S-3
           Filed August 30, 2024
           File No. 333-281891
Dear Thomas Schuetz:

       This is to advise you that we have not reviewed and will not review your
registration
statement.

       Please refer to Rules 460 and 461 regarding requests for acceleration.
We remind you that
the company and its management are responsible for the accuracy and adequacy of
their
disclosures, notwithstanding any review, comments, action or absence of action
by the staff.

       Please contact Tamika Sheppard at 202-551-8346 with any questions.



                                                           Sincerely,

                                                           Division of
Corporation Finance
                                                           Office of Life
Sciences
cc:   Finn Murphy