Exhibit 10.4

  

  

  

  
    AMCI ACQUISITION CORP.

    975 Georges Station Road, Suite 900

    Greensburg, PA 15601

    

    

    November 15, 2018

    

    

    AMCI Holdings, Inc.

    600 Steamboat Road South

    Greenwich, CT 06830

    

    

    Re: Administrative Support Agreement

    

    

    Ladies and Gentlemen:

    

    

    This letter agreement by and between AMCI Acquisition Corp. (the “Company”) and AMCI Holdings, Inc. (“AMCI Holdings”), dated as of the
        date hereof, will confirm our agreement that, commencing on the date the securities of the Company are first listed on The Nasdaq Capital Market (the “Listing Date”), pursuant to a Registration Statement on Form S-1 and prospectus filed with the
        U.S. Securities and Exchange Commission (the “Registration Statement”) and continuing until the earlier of the consummation by the Company of an initial business combination or the Company’s liquidation (in each case as described in the
        Registration Statement) (such earlier date hereinafter referred to as the “Termination Date”):

    

    

    (i) AMCI Holdings shall make available, or cause to be made available, to the Company, at 975 Georges Station Road, Suite 900,
        Greensburg, PA 15601 (or any successor location of AMCI Holdings), certain office space, utilities and secretarial and administrative support as may be reasonably required by the Company. In exchange therefor, the Company shall pay AMCI Holdings
        the sum of $10,000 per month on the Listing Date and continuing monthly thereafter until the Termination Date; and

    

    

    (ii) AMCI Holdings hereby irrevocably waives any and all right, title, interest, causes of action and claims of any kind as a result of,
        or arising out of, this letter agreement (each, a “Claim”) in or to, and any and all right to seek payment of any amounts due to it out of, the trust account established for the benefit of the public stockholders of the Company and into which
        substantially all of the proceeds of the Company’s initial public offering will be deposited (the “Trust Account”) as a result of, or arising out of, this letter agreement, and hereby irrevocably waives any Claim it may have in the future, which
        Claim would reduce, encumber or otherwise adversely affect the Trust Account or any monies or other assets in the Trust Account, and further agrees not to seek recourse, reimbursement, payment or satisfaction of any Claim against the Trust Account
        or any monies or other assets in the Trust Account for any reason whatsoever.

    

    

    This letter agreement constitutes the entire agreement and understanding of the parties hereto in respect of its subject matter and
        supersedes all prior understandings, agreements, or representations by or among the parties hereto, written or oral, to the extent they relate in any way to the subject matter hereof or the transactions contemplated hereby.

    

    

    This letter agreement may not be amended, modified or waived as to any particular provision, except by a written instrument executed by
        the parties hereto.

    

    

    No party hereto may assign either this letter agreement or any of its rights, interests, or obligations hereunder without the prior
        written approval of the other party. Any purported assignment in violation of this paragraph shall be void and ineffectual and shall not operate to transfer or assign any interest or title to the purported assignee.

    

    

    This letter agreement constitutes the entire relationship of the parties hereto, and any litigation between the parties (whether
        grounded in contract, tort, statute, law or equity) shall be governed by, construed in accordance with, and interpreted pursuant to the laws of the State of New York, without giving effect to its choice of law principles.

    

    

    [Signature Page Follows]

     

      

    
      
        


    

    	 	
            Very truly yours,

          
	 	 
	 	
            AMCI ACQUISITION CORP.

          
	 	 	 
	 	
            By:

          	
            /s/ William Hunter

          
	 	 	
            Name: William Hunter

          
	 	 	
            Title: Chief Executive Officer

          


    

    

    AGREED TO AND ACCEPTED BY:

    AMCI HOLDINGS, INC.

    

    

    	
            By:

          	
             /s/ Hans J. Mende

          	 
	 	
            Name: Hans J. Mende

          
	 	
            Title: President

          


    

    

    [Signature Page to Administrative Support Agreement]