STOCK OPTION GRANT NOTICE FOR NON-EMPLOYEE DIRECTORS

Exhibit 10.4

[EXPRESS SCRIPTS HOLDING COMPANY]

STOCK OPTION GRANT NOTICE

FOR NON-EMPLOYEE DIRECTORS

Notice is hereby given of the following option grant (the “Option”) to purchase shares of common stock, $0.01 par value per share, of Express Scripts Holding Company (the “Company”) pursuant to the following terms and conditions:

This Option is granted under, and governed by, the terms and conditions of this Grant Notice, the Plan and the Option Agreement.

Attachments:

Exhibit A—Stock Option Agreement

Exhibit B—Express Scripts Holding Company 2016 Long-Term Incentive Plan

EXHIBIT A

STOCK OPTION AGREEMENT

FOR NON-EMPLOYEE DIRECTORS

Express Scripts Holding Company, a Delaware corporation (“Company”), has granted you (“Optionee”) an option to purchase shares of common stock of the Company, $0.01 par value per share (“Common Stock”), pursuant to the terms and conditions set forth in your Stock Option Grant Notice (“Grant Notice”) and this Stock Option Agreement (“Option Agreement”).

The Option is granted pursuant to the Express Scripts Holding Company 2016 Long-Term Incentive Plan, as amended from time to time (the “Plan”), pursuant to which options, and other awards, may be granted to Non-Employee Directors of the Company. Except as otherwise specifically set forth herein, all capitalized terms utilized herein (including on Schedule 1 hereto) shall have the respective meanings ascribed to them in the Plan

The details of your Option are as follows:

1. Grant of Option. Pursuant to an action of the Board and or a committee authorized by the Board, the Company hereby grants to Optionee an option to purchase shares of Common Stock (the “Option”), subject to the terms and conditions described herein. The number of shares of Common Stock subject to your Option and the Exercise Price Per Share are set forth in the Grant Notice.

2. Term, Vesting and Forfeiture.

(a) Term. This Option may be exercised only within the Term set forth in the Grant Notice, and may be exercised during such Term only in accordance with the Plan and the terms of this Option Agreement.

(b) Time Vesting. The Option shall vest in one or more installments in accordance with the Vesting Schedule set forth on the Grant Notice, with the vesting of each installment subject to the Optionee’s continued service as a member of the Board through the applicable vesting date, subject to the terms hereof.

(c) Accelerated Vesting. Any Option, or portion thereof, which has not yet vested under subparagraph (b) above shall, upon the occurrence of a Change in Control or the termination of the Optionee’s continued service as a member of the Board, vest or be forfeited in accordance with the provisions of the Plan, and the terms of this Agreement (including Schedule 1 hereto).

(d) Forfeiture of Option. If Optionee’s service as a member of the Board terminates for any reason, Optionee shall forfeit all rights with respect to any portion of the Option that has not yet vested as of the effective date of the termination, except to the extent such Award vests upon such termination under Paragraph 2(c).

3. Exercise of Option.

(a) Right to Exercise. This Option is exercisable during its Term in accordance with the Vesting Schedule set forth in the Grant Notice and the applicable provisions of the Plan and this Option Agreement.

(b) Method of Exercise. This Option is exercisable pursuant to the procedures for exercise provided from time to time by the Company and/or by a third-party vendor selected by the Company. The Option exercise shall require payment of the aggregate exercise price as to all exercised shares. The method of payment of the aggregate exercise price shall be in a form approved by the Company in accordance with Section 7(a)(ii) of the Plan. This Option shall be deemed to be exercised upon receipt and approval by the Company (or the appropriate third party) of all required exercise notices, together with full payment of the exercise price and such additional documents as the Company (or the third-party vendor) may then require. The Company may cause, or authorize its third-party to vendor to cause, the vested portion of this Option to automatically be exercised on the Expiration Date for such Option, to the extent it has not previously been exercised or forfeited.

4. Incorporation of the Plan by Reference; Conflicting Terms. The Option is granted under, and expressly subject to, the terms and provisions of the Plan, which terms and provisions are incorporated herein by reference. Optionee hereby acknowledges receipt of a copy of the Plan and agrees to be bound by all the terms and provisions thereof. In the event of any conflict between the terms of the Plan and the terms of this Agreement, the terms and provisions of the Plan shall govern.

5. Non-Transferability of Option. This Option may not be transferred in any manner otherwise than by will or by the laws of descent or distribution and may be exercised during the lifetime of Optionee only by Optionee. The terms of the Plan and this Option Agreement shall be binding upon the executors, administrators, heirs, successors and assigns of Optionee.

6. Stockholder Rights. Optionee shall not have any stockholder rights with respect to the shares of Common Stock granted pursuant to this Option until Optionee shall have exercised the Option in accordance with Section 3 hereof.

7. Adjustments Upon Changes in Capitalization or Corporate Acquisitions. Should any change be made to the Common Stock by reason of any Fundamental Change, divestiture, distribution of assets to stockholders (other than ordinary cash dividends), reorganization, recapitalization, reclassification, stock dividend, stock split, reverse stock split, stock combination or exchange, rights offering, spin-off or other relevant change, appropriate adjustments shall be made to (a) the total number and/or class of securities subject to this Option, and (b) the Exercise Price Per Share set forth in the Grant Notice in order to reflect such change and thereby preclude a dilution or enlargement of benefits hereunder.

8. Compliance with Laws and Regulations. Notwithstanding anything herein to the contrary, no shares of Common Stock shall be issued pursuant to the exercise of this Option unless such issuance and exercise complies with all relevant provisions of law and the requirements of any stock exchange or quotation service upon which the shares of Common Stock are then listed.

9. Board Discretion. This Option has been granted pursuant to a determination made by the Board and/or one or more committees of the Board (as delegated by the Board). Notwithstanding anything to the contrary herein, and subject to the limitations of the Plan, the Board or its delegated committee(s) shall have plenary authority to: (a) interpret any provision of this Agreement or the Option; (b) make any determinations necessary or advisable for the administration of this Agreement or the Option; (c) make adjustments as it deems appropriate to the aggregate number and type of securities available under this Agreement to appropriately adjust for, and give effect to, any Fundamental Change, divestiture, distribution of assets to stockholders (other than ordinary cash dividends), reorganization, recapitalization, reclassification, stock dividend, stock split, reverse stock split, stock combination or exchange, rights offering, spin-off or other relevant change; and (d) otherwise modify or amend any provision hereof, or otherwise with respect to the Option, in any manner that does not materially and adversely affect any right granted to Optionee by the express terms hereof, unless required as a matter of law, subject to the limitations stated in the Plan.

10. Taxes. By accepting this Option pursuant to this Agreement, Grantee represents that he or she has reviewed with his or her own tax advisors the federal, state, local and foreign tax consequences of the transactions contemplated by this Agreement and that he or she is relying solely on such advisors and not on any statements or representations of the Company or any of its agents. Grantee understands and agrees that he or she (and not the Company) shall be responsible for any tax liability that may arise as a result of the transactions contemplated by this Agreement.

11. Electronic Delivery. The Company may choose to deliver certain statutory or regulatory materials relating to the Plan in electronic form, including without limitation securities law disclosure materials. Without limiting the foregoing, by accepting this Option, Optionee hereby agrees that the Company may deliver the Plan prospectus and the Company’s annual report to Optionee in an electronic format. If at any time Optionee would prefer to receive paper copies of any document delivered in electronic form, the Company will provide such paper copies upon written request to the Investor Relations department of the Company.

12. No Right to Continued Service on the Board. Nothing in this Agreement shall be deemed to create any limitation or restriction on or otherwise affect such rights as the Company, the stockholders of the Company, or the Board otherwise would have to remove Optionee from the Board, to exclude Optionee from any slate of nominees for election to the Board, or to otherwise terminate Optionee’s service on the Board at any time for any reason.

13. Entire Agreement. This Agreement, including Schedule 1 hereto, and the Plan contain the entire understanding of the parties with respect to the subject matter hereof and supersede all prior agreements, understandings and negotiations between the parties.

14. Governing Law. To the extent federal law does not otherwise control, this Agreement shall be governed by the laws of Delaware, without giving effect to principles of conflicts of laws.

SCHEDULE 1 TO EXHIBIT A

TERMINATION AND CHANGE IN CONTROL PROVISIONS UNDER THE

EXPRESS SCRIPTS HOLDING COMPANY 2016 LONG-TERM INCENTIVE PLAN

STOCK OPTION GRANT NOTICE

FOR NON-EMPLOYEE DIRECTORS

I. Termination of Service of Non-Employee Director

(A) Generally. Except as provided herein, if Optionee’s service as a member of the Board terminates, then any portion of the Option that has not vested as of the date of such termination shall terminate as of such date, and the unvested portion of the Option shall be forfeited to the Company without payment therefor.

(B) Death. If Optionee’s service as a member of the Board terminates because of his or her death, then the Option, to the extent it has not expired or been terminated, shall vest and become exercisable in full, and may be exercised by the Optionee’s Successor at any time, or from time to time, within one year after the date of Optionee’s death.

(C) Disability. If Optionee’s service as a member of the Board terminates because of Disability, then the Option, to the extent it has not expired or been terminated, shall vest and become exercisable in full, and Optionee or Optionee’s Successor may exercise such Option at any time, or from time to time, within one year after the date of Optionee’s Disability.

(D) Retirement. The termination of Optionee’s service as a member of the Board after attainment of age 65 for any reason other than death or Disability shall be considered a Retirement, subject to the following:

(E) Reasons other than Death, Disability, Tenured Retirement, Early Retirement or Termination for Cause. If Optionee’s service as a member of the Board terminates due to a Standard Retirement or for any other reason other than death, Disability, Tenured Retirement or Early Retirement, then the Option, to the extent it has not expired or been terminated, shall remain exercisable for one year after termination of Optionee’s service on the Board, but only to the extent that such Option was exercisable immediately prior to Optionee’s termination of service.

(F) Expiration of Term. Any portion of the Option that remains unexercisable upon termination of service as a member of the Board (after taking into account the foregoing paragraphs (A)-(E), and except as specifically provided in the foregoing paragraph (D)(3)) shall terminate immediately upon such termination of service as a member of the Board. Any portion of the Option that is, or becomes, exercisable upon termination of service as a member of the Board (or thereafter pursuant to the foregoing paragraph (D)(3)) which is not exercised within the applicable period set forth in the foregoing paragraphs (A)-(E) shall terminate as of the end of the applicable period described in such paragraphs; provided, however, that the Company may cause, or authorize its third-party to vendor to cause, any remaining vested portion of the Option to automatically be exercised on the last date of the applicable period, to the extent it has not previously been exercised or forfeited. Notwithstanding the foregoing, or any other provision of the Plan, the Stock Option Agreement, the Grant Notice, or this Schedule 1, in no event shall the Option be exercisable after expiration of the Term.

II. Change in Control

(A) Acceleration of Vesting Upon Change in Control After Which No Public Market for Company or Exchange Stock Exists

(i) Acceleration of Vesting. Upon the occurrence of a Change in Control after which there will be no generally recognized U.S. public market for the Company’s Common Stock or any common stock for which the Company’s Common Stock is exchanged, the Option, to the extent it has not expired or been terminated, shall, to the extent not yet exercisable, vest and become exercisable in full.

(ii) Company Payment. Upon the occurrence of a Change in Control transaction after which there will be no generally recognized U.S. public market for the Company’s Common Stock or any common stock for which the Company’s Common Stock is exchanged, on the Change in Control

Date the Option shall be automatically cancelled without further action by the Company or the Optionee, and the Company shall provide payment in connection with such cancellation at a per share price equal to the excess (if any) of the Change in Control Price (as defined below) over the exercise price of the Option. The Change in Control Price shall mean the value, expressed in dollars, as of the date of receipt of the per share consideration received by the Company’s stockholders whose stock is acquired in a transaction constituting a Change in Control. In case such all or part of such consideration shall be in a form other than cash, the value of such consideration shall be as determined in good faith by a majority of the Board of Directors based on a written opinion by a nationally recognized investment banking firm, whose determination shall be described in a statement furnished to Participants.

(B) Acceleration of Vesting Upon Other Change in Control Transactions. Upon the occurrence of a Change in Control after which there remains a generally recognized U.S. public market for the Company’s Common Stock or for any common stock for which the Company’s Common Stock is exchanged, the Option, to the extent it has not expired or been terminated, shall vest and become exercisable in full and shall remain exercisable for the remainder of the Term.

(C) Options Not Assumed. Notwithstanding anything herein to the contrary, the Board may provide for such other treatment of the Option as the Board may determine in its sole discretion with respect to the Option if it is not assumed or is cancelled in connection with a Change in Control.