Consulting Agreement by and between the Registrant and Michael Vasconcelles dated as of July 25, 2019

Exhibit 10.3

CONSULTING AGREEMENT

This Consulting Agreement (“Agreement”) is made between Unum Therapeutics Inc., a Delaware corporation (the “Company”), and Michael Vasconcelles, M.D. (the “Consultant,” and, together, with the Company, the “Parties”).

WHEREAS, the Consultant has been employed by the Company pursuant to the terms of an Employment Agreement which became effective upon the date of the Company’s initial public offering (the “Employment Agreement”) as well as the Invention Assignment, Non-Disclosure and Business Protection Agreement dated September 22, 2015 (the “BPA”);

WHEREAS, the Consultant remains fully obligated to comply with the terms of Section 7 of the Employment Agreement as well as the BPA (the “Continuing Obligations”);

WHEREAS, the Consultant resigned from his employment with the Company without Good Reason pursuant to Section 3(e) of the Employment Agreement and the Date of Termination for purposes of the Employment Agreement shall be July 12, 2019;

WHEREAS, Consistent with the terms of the Company’s 2018 Stock Option and Incentive Plan (as may be amended the “Plan” and, collectively, with any stock option award agreement the “Equity Documents”) the Consultant’s outstanding equity interests granted to him prior to the Date of Termination shall cease vesting on the Date of Termination and shall lapse;

WHEREAS, effective on the date following Date of Termination (the “Effective Date”), the Company desires to engage the Consultant as an independent contractor to provide outside, professional services in the areas of his professional expertise, and the Consultant wishes to furnish such services, on the terms and conditions set forth herein.

NOW THEREFORE, in consideration of the mutual covenants and promises contained herein and other good and valuable consideration, the receipt and sufficiency of which is hereby acknowledged by the parties hereto, the parties agree as follows:

1.Services.

(a)The Company has requested, and the Consultant has agreed to perform, consulting services on an as-needed basis as reasonably requested by the Company (the “Services”) from time to time during the Consulting Period (as defined below), which the Parties agree shall include certain quarterly commitments related to the Company’s clinical requirements and obligations, and that the Consultant shall devote an average of approximately fifteen (15) days annually to the performance of the Services.

(b)The Consultant may not subcontract or sublicense any rights or obligations under this Agreement without the prior written consent of the Company.

(c)The Consultant shall keep the Company fully informed concerning the progress of the Services to be performed hereunder. The Consultant shall provide such reports, or participate in telephone conferences and meetings, as the Company may reasonably request.

2.Consulting Period. The Consultant shall be engaged by the Company pursuant to this Agreement commencing as of the Effective Date and continuing for two years thereafter (the “Consulting Period”) unless such consultancy is terminated earlier in accordance with the provisions of Section of this Agreement.

3.Terms.

(a)Equity. Subject to approval by the Board, in exchange for the Consultant’s provision of the Services during the Consulting Period, the Company shall grant the Consultant an option to purchase 100,000 shares of the Company’s common stock (the “Consultancy Option Award”). The exercise price per share of the Consultancy Option Award will be the fair market value as determined by the Board when the Consultancy Option Award is granted. The Consultancy Option Award will be subject to the terms of and contingent upon the Consultant’s execution of a stock option award agreement issued pursuant to the Plan. The Consultancy Option Award shall become vested and exercisable over a two-year period, vesting in equal quarterly installments with the first quarterly installment (i.e., 12.5%) to vest on October 1, 2019 and the final quarterly installment to vest on July 1, 2021, contingent upon the Consultant remaining engaged with the Company pursuant to this Agreement through each applicable vesting date.

(a)Expenses. The Company shall reimburse the Consultant for all reasonable and necessary expenses incurred or paid by the Consultant solely in connection with, or directly related to, the performance of the Consultant’s Services under this Agreement.

(b)Benefits. The Consultant shall not be entitled to any benefits, coverages or privileges, including, without limitation, social security, unemployment, medical or pension payments, made available to employees of the Company.

(c)Taxes. The Consultant shall be responsible for and liable for all taxes, excises, assessments, insurance and any benefits including, but not limited to health, accident and compensation benefits and shall pay all taxes and contributions, which the Consultant may be required to pay relating to the performance of Services.

4.Term and Termination. The Consulting Period is for a term of two years beginning on the Effective Date, unless terminated earlier under the following circumstances:

(a)The Company may, without prejudice to any right or remedy it may have due to any failure of the Consultant to perform the Consultant’s obligations under this Agreement, terminate this Agreement and the Consultant may terminate this Agreement in either case for any reason upon not less than fifteen (15) days’ prior written notice which may be waived by the Company in its sole discretion. In the event of such termination, the Consultant shall be entitled to expenses paid or incurred prior to the effective date of termination and vesting shall cease as of the termination date.

(b)Consequences of Termination. Upon the termination of this Agreement for any reason, the Consultant agrees to immediately (i) discontinue any further Services hereunder, except to the extent that Consultant and Company may otherwise agree in writing, and (ii) return all Company property in Consultant’s possession, including, without limitation, any laptop computer or other devices, without any deletions or alterations to content. For the avoidance of doubt, Consultant’s options shall cease vesting as of the last day of the Consulting Period or upon termination of this Agreement, if earlier, and Consultant will have three months from the last day of the Consulting Period or the termination of this Agreement, if earlier, to exercise any then vested options consistent with the terms of the Equity Documents. Any portion of the Consultancy Option Award that is not exercisable on the date of termination of this Agreement, if earlier than the last day of the Consulting Period, shall terminate immediately and be of no further force or effect.

(c)If the Parties wish to extend the term of this Agreement beyond the Consulting Period, they may do so by mutual agreement.

5.Cooperation. The Consultant shall use his best efforts in the performance of the Consultant’s obligations under this Agreement. The Company shall provide such access to its information and property as may be reasonably required in order to permit the Consultant to perform Consultant’s obligations hereunder, provided, however, that the Consultant shall acquire no right or license in such Company information and property. The Consultant shall cooperate with the Company’s personnel, shall not interfere with the conduct of the Company’s business and shall

observe all rules, regulations and security requirements of the Company concerning the safety of persons and property.

6.Restrictive Covenants.

(a)Proprietary Information.

(i)The Consultant acknowledges that the Consultant’s relationship with the Company is one of high trust and confidence and that in the course of the Consultant’s service to the Company, Consultant will have access to and contact with Proprietary Information (as defined below). The Consultant agrees that the Consultant will not, during the Consulting Period or at any time thereafter, disclose to others, or use for the Consultant’s benefit or the benefit of others, any Proprietary Information or Invention (as defined below). Any Proprietary Information may only be used by the Consultant solely to perform the Services for the benefit of the Company. Further, the Consultant shall treat the Proprietary Information with the same degree of security and confidentiality with which it maintains its own confidential information, but in no case shall undertake less than commercially reasonable efforts to protect Proprietary Information.

(ii)For purposes of this Agreement, “Proprietary Information” shall mean, by way of illustration and not limitation, all information (whether or not patentable and whether or not copyrightable) owned, possessed or used by the Company, whether or not marked as confidential or proprietary, including, without limitation, any Invention, formula, vendor information, customer information, apparatus, equipment, trade secret, process, research, report, technical data, know-how, computer program, software, software documentation, hardware design, technology, marketing or business plan, forecast, unpublished financial statement, budget, license, price, cost and employee list that is communicated to, learned of, developed or otherwise acquired by the Consultant in the course of service as a consultant to the Company.

(iii)The Consultant’s obligations under this Section 6(a) shall not apply to any information that (A) is or becomes known to the general public under circumstances involving no breach by the Consultant or others of the terms of this Section 6(a), (B) is generally disclosed to third parties by the Company without restriction on such third parties, or (C) is approved for release by written authorization of the Board of Directors of the Company.

(iv)Upon termination of this Agreement or at any other time upon request by the Company, the Consultant shall promptly deliver to the Company all records, files, memoranda, notes, designs, data, reports, price lists, customer lists, drawings, plans, computer programs, software, software documentation, sketches, laboratory and research notebooks and other documents (and all copies or reproductions of such materials) relating to the business of the Company.

(v)The Consultant represents that the Consultant’s retention as a consultant with the Company and the Consultant’s performance under this Agreement does not, and shall not, breach any agreement that obligates the Consultant to keep in confidence any trade secrets or confidential or proprietary information of the Consultant’s or of any other party or to refrain from competing, directly or indirectly, with the business of any other party. The Consultant shall not disclose to the Company any trade secrets or confidential or proprietary information of any other party.

(vi)The Consultant acknowledges that the Company from time to time may have agreements with other persons or with the United States Government, or agencies thereof, that impose obligations or restrictions on the Company regarding inventions made during the course of work under such agreements or regarding the confidential nature of such work. The Consultant agrees to be bound by all such obligations and restrictions that are known to the Consultant and to take all action necessary to discharge the obligations of the Company under such agreements.

(vii)The Consultant acknowledges and agrees that the Consultant shall have no right to publish any articles, or make any public disclosures pertaining to the Inventions or the Services hereunder, or to use

or disclose the name, logo or other trademark or service mark of the Company for any purpose, without the prior written consent of the Company in each instance, which may be withheld in the sole discretion of the Company.

(b)Documents, Records, etc. All documents, records, data, apparatus, equipment and other physical property which are furnished to the Consultant by the Company or are produced by the Consultant in connection with the Consultant’s engagement will be and remain the sole property of the Company. The Consultant will return to the Company all such materials and property as and when requested by the Company. In any event, the Consultant will return all such materials and property immediately upon termination of the Consultant’s engagement for any reason. The Consultant will not retain any such material or property or any copies thereof after such termination.

(c)Inventions.

(i)All inventions, ideas, discoveries, computer programs, data, technology, designs, innovations, processes, know-how, concepts, prototypes, samples, models, technical information, drawings, specifications, improvements and the like (whether or not patentable and whether or not copyrightable) (“Inventions”) which are made, conceived, invented, reduced to practice, created, written, designed or developed by the Consultant, solely or jointly with others and whether during normal business hours or otherwise, (A) during the Consulting Period if related to the business of the Company or (B) after the Consulting Period if resulting from or directly derived from Proprietary Information (as defined below), shall be the sole and exclusive property of the Company. The Consultant agrees to assign, and hereby irrevocably assigns, sells, transfers and sets over to the Company and its successors and assigns all of Consultant’s world-wide right, title and interest in and to the Inventions and the Invention Records (defined below) and any and all related patents, copyrights, trademarks, trade names, trade secrets and other industrial and intellectual property rights and applications therefor, together with the rights to all income derived from said Inventions and Invention Records, including the right to sue in the name of Company for past or future infringement thereof and to recover all damages therefrom. To the extent any of the Consultant’s rights in the Inventions or Invention Records are not capable of assignment under applicable law or otherwise, the Consultant hereby irrevocably and unconditionally waives all enforcement of such rights to the maximum extent permitted under applicable law. To the extent such waiver is deemed unenforceable under applicable law, the Consultant hereby grants to Company, an exclusive, perpetual, irrevocable, transferable, assignable, fully paid-up and royalty-free license to copy, modify, perform, display, create derivative works based on, make, have made, sell and have sold, and otherwise use in any manner, such Inventions and Invention Records, including the right to sub-license to any third party.

(ii)The Consultant hereby appoints any officer of the Company as the Consultant’s duly authorized attorney to execute, file, prosecute and protect the Inventions and Invention Records before any domestic or foreign government agency, court or authority. Upon the request of the Company and at the Company’s expense, the Consultant shall execute such further assignments, documents and other instruments as may be necessary or desirable to fully and completely assign all Inventions and Invention Records to the Company and to assist the Company in applying for, obtaining and enforcing patents or copyrights or other rights in the United States and in any foreign country with respect to any Invention or Invention Record. The Consultant also hereby waives all claims to moral rights in any Inventions and Invention Records.

(iii)The Consultant shall promptly disclose to the Company all Inventions and will maintain complete, adequate and current written records (in the form of notes, sketches, drawings and as may be specified by the Company) to document the conception and/or first actual reduction to practice of any Invention (collectively, “Invention Records”). Such written Invention Records shall be available to and remain the sole and exclusive property of the Company at all times. The Consultant shall ensure that any and all Invention Records arising out of or in any way related to the Company, the Services or the Inventions shall not be comingled with the written records pertaining to any other project on which the Consultant may be working.

(iv)The Consultant shall not include any third party or pre-existing intellectual property of Consultant created outside the scope of or prior to this Agreement (collectively “Other Inventions”) in the Inventions without the prior written consent of Company. To the extent that Company grants such consent to include

Other Inventions, the Consultant hereby grants to the Company a perpetual, worldwide, royalty-free, irrevocable, transferable, sublicensable, assignable, license to use, copy, distribute, perform, display, maintain, modify, make, have made, sell and have sold such Other Inventions.

(d)Injunction. The Consultant agrees that it would be difficult to measure any damages caused to the Company which might result from any breach by the Consultant of the promises set forth in this Section 6, and that in any event money damages would be an inadequate remedy for any such breach. The Consultant agrees, therefore, that, in addition to any other remedy it may have, the Company shall be entitled to enforce the specific performance of this Agreement by the Consultant and to seek and obtain both temporary and permanent injunctive relief (to the extent permitted by law) without the necessity of proving actual damages or posting bond.

7.Consent to Jurisdiction. The parties hereby consent to the jurisdiction of the Superior Court of the Commonwealth of Massachusetts and the United States District Court for the District of Massachusetts. Accordingly, with respect to any such court action, the Consultant (a) submits to the personal jurisdiction of such courts; (b) consents to service of process; and (c) waives any other requirement (whether imposed by statute, rule of court, or otherwise) with respect to personal jurisdiction or service of process.

8.Integration. This Agreement constitutes the entire agreement between the parties with respect to the subject matter hereof and supersedes all prior agreements between the parties concerning such subject matter, provided that this Agreement shall not affect the Continuing Obligations (including Section 7 of the Employment Agreement and the BPA, the terms of which are incorporated by reference herein) and the Equity Documents.

9.Successors and Assigns. This Agreement shall be binding upon, and inure to the benefit of, both parties and their respective successors and assigns (including the Consultant’s heirs in the event of his death), including any corporation with which, or into which, the Company may be merged or which may succeed to its assets or business, provided, however, that the obligations of the Consultant are personal and shall not be assigned by the Consultant.

10.Enforceability. If any portion or provision of this Agreement (including, without limitation, any portion or provision of any section of this Agreement) shall to any extent be declared illegal or unenforceable by a court of competent jurisdiction, then the remainder of this Agreement, or the application of such portion or provision in circumstances other than those as to which it is so declared illegal or unenforceable, shall not be affected thereby, and each portion and provision of this Agreement shall be valid and enforceable to the fullest extent permitted by law.

11.Survival. The provisions of this Agreement shall survive the termination of this Agreement and/or the termination of the Consultant’s engagement to the extent necessary to effectuate the terms contained herein.

12.Waiver. No waiver of any provision hereof shall be effective unless made in writing and signed by the waiving party. The failure of any party to require the performance of any term or obligation of this Agreement, or the waiver by any party of any breach of this Agreement, shall not prevent any subsequent enforcement of such term or obligation or be deemed a waiver of any subsequent breach.

13.Notices. Any notices, requests, demands and other communications provided for by this Agreement shall be sufficient if in writing and delivered in person or sent by a nationally recognized overnight courier service or by registered or certified mail, postage prepaid, return receipt requested, to the Consultant at the last address the Consultant has filed in writing with the Company or, in the case of the Company, at its main offices, attention of the Board.

14.Amendment. This Agreement may be amended or modified only by a written instrument signed by the Consultant and by a duly authorized representative of the Company.

15.Governing Law. This is a Massachusetts contract and shall be construed under and be governed in all respects by the laws of the Commonwealth of Massachusetts, without giving effect to the conflict of laws principles of such Commonwealth. With respect to any disputes concerning federal law, such disputes shall be determined in

accordance with the law as it would be interpreted and applied by the United States Court of Appeals for the First Circuit.

16.Counterparts. This Agreement may be executed in any number of counterparts, each of which when so executed and delivered shall be taken to be an original; but such counterparts shall together constitute one and the same document.

17.Gender Neutral. Wherever used herein, a pronoun in the masculine gender shall be considered as including the feminine gender unless the context clearly indicates otherwise.

IN WITNESS WHEREOF, the Parties have executed this Agreement effective on the date and year first above written.