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                               September 30, 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. 2 to
Proxy Statement on Schedule 14A
                                                            Filed September 22,
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 Preliminary Proxy Statement on Schedule 14A

       Overview of KIQ, page 25

   1.                                                   We note your disclosure
that Kiq was formed on April 28, 2020 and that prior to its
                                                        acquisition by Unum,
Kiq never had any employees or facilities and only had one asset, an
                                                        exclusive License
Agreement, and that Kiq had no assembled workforce or processes in
                                                        place to perform the
development of the license. Given this disclosure, please revise to
                                                        clarify the basis for
your disclosure that PLX9486 was    Kiq   s most advanced program
                                                        and is a    highly
potent and selective    KIT D816V inhibitor.
   2.                                                   It does not appear that
you have filed the exclusive License Agreement with Plexxicon
                                                        Inc. as an exhibit to
any of your filings. Please file that agreement as an exhibit to an
                                                        appropriate filing or
explain to us the basis for your determination that it is not required to
                                                        be filed. If you
believe the agreement is not required to be filed, please include in your
                                                        explanation a detailed
analysis supporting your belief that your plans to develop PLX9486
                                                        are not substantially
dependent on the license agreement.
 Charles Wilson, Ph.D.
Unum Therapeutics Inc.
September 30, 2020
Page 2
If our efforts to protect the proprietary nature of the intellectual property
related to our
technologies..., page 74

3.     Please revise to clarify if the patents disclosed in this risk factor
relate to your ACTR
       technologies and revise to clarify any material risks related to the
technology licensed
       under the agreement with Plexxikon, Inc.
Sales of a substantial number of shares of our common stock, page 99

4.     Please update this risk factor to address the number of shares
registered for resale under
       your recently filed registration statement on Form S-3.
Principal Stockholders, page 110

5.     Please disclose the natural person who beneficially own the shares held
in the name of the
       legal entities identified in your table in this section.
        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
September 30, 2020 Page 2
cc:       Andrew H. Goodman, Esq.
FirstName LastName