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                              October 5, 2020

       Charles Wilson, Ph.D.
       President and Chief Executive Officer
       Unum Therapeutics Inc.
       200 Cambridge Park Drive, Suite 3100
       Cambridge, Massachusetts 02140

                                                        Re: Unum Therapeutics
Inc.
                                                            Amendment No. 3 to
Proxy Statement on Schedule 14A
                                                            Filed October 2,
2020
                                                            File No. 001-38443

       Dear Dr. Wilson:

              We have reviewed your amended filing and have the following
comments. In some of
       our comments, we may ask you to provide us with information so we may
better understand your
       disclosure.

              Please respond to these comments within ten business days by
providing the requested
       information or advise us as soon as possible when you will respond. If
you do not believe our
       comments apply to your facts and circumstances, please tell us why in
your response.

                                                        After reviewing your
response to these comments, we may have additional comments.

       Amendment No. 2 to Proxy Statement on Schedule 14A

       Overview of Kiq, page 25

   1.                                                   We note your revised
disclosure in response to prior comment 1 that PLX9486 was in
                                                        Phase II clinical
development and the disclosure that this product candidate is a    highly
                                                        potent    inhibitor.
Please remove all statements that present your conclusions regarding
                                                        the efficacy of your
product candidate as this is a determination within the authority of the
                                                        U.S. Food and Drug
Administration and comparable regulatory bodies.
   2.                                                   We note that in
response to prior comment 2 you have included a redacted version of the
                                                        license agreement with
Plexxicon Inc. as annex to your proxy statement. Since it does not
                                                        appear that you have
filed the license agreement as an exhibit to one of the forms under
                                                        the Securities Act or
the Exchange Act that are designated in Item 601 of Regulation S-K,
                                                        it is unclear which
rule or regulation you are relying on to redact provisions from this
                                                        agreement. Please
advise. Please also disclose the aggregate amounts paid or received to
                                                        date under agreement
and the aggregate future potential milestone payments to be paid
 Charles Wilson, Ph.D.
Unum Therapeutics Inc.
October 5, 2020
Page 2
      under the license agreement.
        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 Tim Buchmiller at (202) 551-3635 or Celeste Murphy at
(202) 551-3257
with any questions.



                                                          Sincerely,
FirstName LastNameCharles Wilson, Ph.D.
                                                          Division of
Corporation Finance
Comapany NameUnum Therapeutics Inc.
                                                          Office of Life
Sciences
October 5, 2020 Page 2
cc:       Andrew H. Goodman, Esq.
FirstName LastName