Exhibit (a)(1)(D)

Offer to Purchase

All Outstanding Shares of Common Stock

of

Poseida Therapeutics, Inc.

at

$9.00 per share in cash, plus one non-transferable contingent value right per share representing the right to receive certain contingent payments of up to an aggregate amount of $4.00 per share in cash on the achievement of specified milestones on or prior to the applicable milestone outside dates

pursuant to the Offer to Purchase

dated December 9, 2024

by

Blue Giant Acquisition Corp.

a wholly owned subsidiary of

Roche Holdings, Inc.

THE OFFER AND WITHDRAWAL RIGHTS EXPIRE AT ONE MINUTE FOLLOWING 11:59 P.M., NEW YORK CITY TIME, ON TUESDAY, JANUARY 7, 2025, UNLESS THE OFFER IS EXTENDED OR EARLIER TERMINATED.

December 9, 2024

To Brokers, Dealers, Commercial Banks, Trust Companies and Other Nominees:

We have been engaged by Blue Giant Acquisition Corp., a Delaware corporation (“Offeror”) and a wholly owned subsidiary of Roche Holdings, Inc., a Delaware corporation (“Parent”), to act as the information agent (the “Information Agent”) in connection with Offeror’s offer to purchase all outstanding shares of common stock, par value $0.0001 per share (the “Shares”), of Poseida Therapeutics Inc., a Delaware corporation (“Poseida”), for (i) $9.00 per Share, in cash, without interest (the “Cash Amount”) less any applicable withholding taxes, plus (ii) one non-transferable contingent value right (each, a “CVR”) per Share, representing the right to receive certain contingent payments of up to an aggregate amount of $4.00 per Share, in cash, without interest less any applicable withholding taxes, upon the achievement of certain specified milestones on or prior to the applicable milestone outside dates in the Contingent Value Rights Agreement, (the “CVR Agreement”) to be entered into with a rights agent mutually agreeable to Parent and Poseida (the Cash Amount plus the CVR, collectively, or any different amount that may be paid pursuant to the Offer to the extent permitted under the Merger Agreement (as defined below), the “Offer Consideration”), upon the terms and subject to the conditions set forth in the Offer to Purchase dated December 9, 2024 (as it may be amended or supplemented from time to time, the “Offer to Purchase”) and the related Letter of Transmittal (as it may be amended or supplemented from time to time, the “Letter of Transmittal” and, together with the Offer to Purchase, the “Offer”) enclosed herewith.

Please furnish copies of the enclosed materials to those of your clients for whose accounts you hold Shares registered in your name or in the name of your nominee.

Enclosed herewith for your information and forwarding to your clients for whose accounts you hold Shares registered in your name or in the name of your nominee are copies of the following documents:

1. The Offer to Purchase.

2. The related Letter of Transmittal for your use in accepting the Offer and tendering Shares and for the information of your clients, together with the included IRS Form W-9 and instructions providing information relating to federal income tax backup withholding. Facsimile copies of the Letter of Transmittal may be used to tender Shares.

3. Notice of Guaranteed Delivery to be used to accept the Offer if certificates for Shares and all other required documents cannot be delivered to Citibank, N.A., the depositary for the Offer (the “Depositary”), or if the procedures for book-entry transfer cannot be completed, prior to the expiration of the Offer.

4. A form of letter which may be sent to your clients for whose accounts you hold Shares registered in your name or in the name of your nominee, with space provided for obtaining such clients’ instructions with regard to the Offer.

5. Poseida’s Solicitation/Recommendation Statement on Schedule 14D-9 dated December 9, 2024.

YOUR PROMPT ACTION IS REQUESTED. WE URGE YOU TO CONTACT YOUR CLIENTS AS PROMPTLY AS POSSIBLE. PLEASE NOTE THAT THE OFFER AND WITHDRAWAL RIGHTS EXPIRE AT ONE MINUTE FOLLOWING 11:59 P.M., NEW YORK CITY TIME, ON JANUARY 7, 2025, UNLESS THE OFFER IS EXTENDED OR EARLIER TERMINATED.

The Offer is being made pursuant to the Agreement and Plan of Merger, dated as of November 25, 2024 (as may be amended or supplemented from time to time, the “Merger Agreement”), among Poseida, Parent and Offeror. The Merger Agreement provides that, among other things, following the completion of the Offer and the satisfaction or waiver of certain conditions set forth in the Merger Agreement, Offeror will merge with and into Poseida (the “Merger”), with Poseida continuing as the surviving corporation and a wholly owned subsidiary of Parent. At the effective time of the Merger, each outstanding Share (other than Shares held in the treasury of Poseida or owned by Poseida, Parent, Offeror or any direct or indirect subsidiary of Poseida, Parent or Offeror, or any stockholders who are entitled to and have properly exercised and perfected a demand for appraisal of such Shares in accordance with Section 262 of the Delaware General Corporation Law (the “DGCL”)) will be cancelled and converted into the right to receive the Offer Consideration. The Merger Agreement is more fully described in Section 13 of the Offer to Purchase.

The Board of Directors of Poseida (the “Poseida Board”) has unanimously (i) determined that the transactions contemplated by the Merger Agreement and the CVR Agreement, including the Offer and the Merger, are advisable and fair to, and in the best interests of Poseida and its stockholders; (ii) approved the execution, delivery and performance by Poseida of the Merger Agreement and the consummation of transactions contemplated thereby, including the Offer and the Merger, and approved the CVR Agreement and the transactions contemplated thereby; (iii) resolved that the Merger will be effected under Section 251(h) of the DGCL; and (iv) resolved to recommend that Poseida’s stockholders accept the Offer and tender their Shares to Offeror pursuant to the Offer. Poseida has been advised that all of its directors and executive officers currently intend to tender, or cause to be tendered pursuant to the Offer, all of their transferrable Shares held of record and beneficially owned by such persons immediately prior to the expiration of the Offer. The foregoing does not include any Shares over which, or with respect to which, any such executive officer or director acts in a fiduciary or representative capacity or is subject to the instructions of a third party with respect to such tender.

The Offer is not subject to any financing condition. The conditions to the Offer are described in Sections 15 and 16 of the Offer to Purchase.

Offeror will not pay any fees or commissions to any broker, dealer or any other person (other than to the Information Agent and the Depositary as described in the Offer to Purchase) for soliciting tenders of Shares pursuant to the Offer. Offeror will, however, upon request, reimburse brokers, dealers, commercial banks, trust companies and other nominees for reasonable and necessary costs and expenses incurred by them in forwarding the enclosed materials to their clients.

Offeror will pay all stock transfer taxes applicable to its purchase of Shares pursuant to the Offer, subject to Instruction 6 of the Letter of Transmittal.

In order to take advantage of the Offer, a properly completed and duly executed Letter of Transmittal (or a manually signed facsimile thereof), with any required signature guarantees, or an Agent’s Message (as defined in

the Offer to Purchase) in connection with a book-entry transfer of Shares, and any other required documents required by the Letter of Transmittal or other customary documents required by the Depositary, should be sent to the Depositary, and certificates representing the tendered Shares should be delivered or such Shares should be tendered by book-entry transfer, all in accordance with the instructions contained in the Letter of Transmittal and the Offer to Purchase.

If holders of Shares wish to tender, but it is impracticable for them to forward their certificates or other required documents or to complete the procedures for delivery by book-entry transfer prior to the expiration of the Offer, a tender may be effected by following the guaranteed delivery procedures described in Section 3 of the Offer to Purchase.

Any inquiries you may have with respect to the Offer should be addressed to, and additional copies of the enclosed materials may be obtained from, the undersigned at the address and telephone number set forth on the back cover of the Offer to Purchase.

Very truly yours,

MacKenzie Partners, Inc.

NOTHING CONTAINED HEREIN OR IN THE ENCLOSED DOCUMENTS SHALL RENDER YOU THE AGENT OF PARENT, OFFEROR, THE INFORMATION AGENT OR THE DEPOSITARY, OR ANY AFFILIATE OF ANY OF THEM, OR AUTHORIZE YOU OR ANY OTHER PERSON TO USE ANY DOCUMENT OR MAKE ANY STATEMENT ON BEHALF OF ANY OF THEM IN CONNECTION WITH THE OFFER OTHER THAN THE DOCUMENTS ENCLOSED HEREWITH AND THE STATEMENTS CONTAINED THEREIN.