Joinder & Second Amendment to Amended & Restated Investor Rights Agreement, by and among BBAI, AE BBAI Aggregator, LP, BBAI Ultimate Holdings, LLC, Seller and the other parties thereto, dated as of December 6, 2021, as amended on July 20, 2023, effective as of February 29, 2024

Exhibit 10.1

JOINDER & SECOND AMENDMENT TO

AMENDED & RESTATED

INVESTOR RIGHTS AGREEMENT

THIS JOINDER & SECOND AMENDMENT TO THE AMENDED & RESTATED INVESTOR RIGHTS AGREEMENT (this “Amendment”) is made as of February 29, 2024, by and among (i) BigBear.ai Holdings, Inc., a Delaware corporation f/k/a GigCapital4, Inc. (the “Company”), (ii) AE BBAI Aggregator, LP, a Delaware limited partnership (“AE Aggregator”), (iii) BBAI Ultimate Holdings, LLC, a Delaware limited liability company (“Ultimate Holdings,” together with AE Aggregator and any of their Permitted Transferees that have executed a joinder to the Investor Rights Agreement (as defined below), the “Partners” and each a “Partner”), and (iv) Pangiam Ultimate Holdings, LLC, a Delaware limited liability company (“Pangiam”). Reference is hereby made to the Amended & Restated Investor Rights Agreement, dated December 6, 2021 (the “Investor Rights Agreement”), by and among (i) the Company, (ii) the Partners, (iii) GigAcquisitions4, LLC, a Delaware limited liability company (the “Sponsor”), (iv) Oppenheimer & Co. Inc. and Nomura Securities International, Inc. (together, the “Original Underwriter Representatives”), (v) William Blair & Company, L.L.C. and BMO Capital Markets Corp. (together with the Original Underwriter Representatives, the “Financial Services Representatives”), and (vi) the Persons listed as Other Holders on the signature pages thereto and each other Person who executes a joinder as an “Other Holder,” as amended by the First Amendment to Amended & Restated Investor Rights Agreement, dated July 20, 2023, by and among (i) the Company, (ii) the Partners, (iii) the Sponsor and (iv) the Financial Services Representatives. All capitalized terms not defined herein shall have the same meaning ascribed to them in the Investor Rights Agreement.

RECITALS

A. Pangiam represents and warrants that it has acquired 61,838,072.00 shares of Common Stock.

B. Pangiam wishes to join and become a “Party” to the Investor Rights Agreement as a “Holder” and an “Other Holder” thereunder and the Company wishes to accept Pangiam as a “Party” thereto and a “Holder” and an “Other Holder” thereunder, all on the terms of the Investor Rights Agreement as amended by this Amendment.

C. Pangiam is executing and delivering this Amendment as a joinder to the Investor Rights Agreement, whereupon Pangiam will be treated as a Party and Holder for all purposes of the Investor Rights Agreement.

D. Section 5.4 of the Investor Rights Agreement provides that any term thereof may be amended by the written consent of (i) the Company, (ii) for so long as the Partners collectively Beneficially Own Common Stock representing 10% or more of the Common Stock Beneficially Owned by the Partners immediately after the Closing, the Partners, and (iii) in any event, at least the Holders holding in the aggregate more than fifty percent (50%) of the Registrable Securities Beneficially Owned by the Holders.

E. The Partners (i) collectively Beneficially Own Common Stock representing more than 10% of the Common Stock Beneficially Owned by the Partners immediately after the Closing and (ii) hold in the aggregate more than fifty percent (50%) of the Registrable Securities Beneficially Owned by the Holders.

F. The Company and the Partners now desire to amend the Investor Rights Agreement to grant registration rights to Pangiam pursuant to the Investor Rights Agreement and to include Pangiam within the definition of “Party” and “Holder” thereunder.

NOW THEREFORE, in consideration of the foregoing premises and certain other good and valuable consideration, the receipt and sufficiency of which are hereby acknowledged, the parties hereby agree as follows:

1. Pangiam hereby acknowledges and agrees that Pangiam has received and read the Investor Rights Agreement, and each of the parties to this Amendment here acknowledge and agree that (a) Pangiam hereby joins and becomes a “Party” to the Investor Rights Agreement and a “Holder” thereunder and (b) Pangiam will be treated as a Party and Holder of Registrable Securities for all purposes of the Investor Rights Agreement, as amended by this Amendment.

AGREEMENT

1. Definitions. The definition of “Shelf Take-Down Initiating Holders” shall be hereby amended and restated in its entirety to read as follows:

“Shelf Take-Down Initiating Holders” means (a) the Partners and Pangiam Ultimate Holdings, LLC and (b) solely with respect to Non-Underwritten Shelf Take-Downs, the other Shelf Holders.

2. Section 3.2(a). Section 3.2(a) of the Investor Rights Agreement shall be hereby amended and restated in its entirety to read as follows:

“(a) Holders’ Demand for Registration. If, at a time when all of the Partners’ and Pangiam Ultimate Holdings, LLC’s Registrable Securities are not included on an effective Shelf Registration Statement, PubCo shall receive from the Partners or Pangiam Ultimate Holdings, LLC at any time following the Lock-up Period (the then eligible Holders, the “Demand Initiating Holders”) a written demand that PubCo effect any Registration (a “Demand Registration”) of Registrable Securities held by such Holders, PubCo will:

(i) use its reasonable best efforts to effect such registration as soon as practicable as will permit or facilitate the sale and distribution of all or such portion of the Demand Initiating Holders Registrable Securities as are specified in such demand; provided, that PubCo shall not be obligated to file any Registration Statement or other disclosure document pursuant to this Section 3.2 (but shall be obligated to continue to prepare such Registration Statement or other disclosure document) if PubCo shall furnish to the Demand Initiating Holders a certificate signed by the chief executive officer or equivalent senior executive of PubCo, stating that the filing or effectiveness of such Registration Statement would require PubCo to make an Adverse Disclosure, in which case PubCo shall have an

additional period (each, a “Demand Delay”) of not more than forty-five (45) days within which to file such Registration Statement; provided, however, that PubCo shall not exercise, in any twelve (12) month period, (x) more than one (1) Demand Delay pursuant to this Section 3.2(a)(i) and Shelf Suspension pursuant to Section 3.1(c) in the aggregate, unless consented in writing by the Demand Initiating Holders or (y) aggregate Demand Delays pursuant to this Section 3.2(a)(i) and Shelf Suspensions pursuant to Section 3.1(c) of more than ninety (90) days. Each Holder shall keep confidential the fact that a Demand Delay is in effect, the certificate referred to above and its contents for the permitted duration of the Demand Delay or until otherwise notified by PubCo, except (A) for disclosure to the Holder’s employees, agents and professional advisers who need to know such information and are obligated to keep it confidential, (B) for disclosures to the extent required in order to comply with reporting obligations to its limited partners who have agreed to keep such information confidential and (C) as required by Law.”

3. Miscellaneous.

3.1 Effect of Amendment. Except as set forth in this Amendment, the provisions of the Investor Rights Agreement shall remain unchanged and shall continue in full force and effect.

3.2 Entire Amendment. This Amendment and the Investor Rights Agreement constitute the entire agreement between the parties hereto pertaining to the subject matter hereof, and any and all other written or oral agreements relating to the subject matter hereof existing between the parties hereto are expressly cancelled.

3.3 Counterparts. This Amendment may be executed in any number of counterparts each of which shall be considered an original and all of which together shall constitute one and the same instrument.

(Signature Page Follows)

IN WITNESS WHEREOF, this Amendment has been executed as of the date and year first written above.

[Second Amendment to Amended & Restated Investor Rights Agreement]

[Second Amendment to Amended & Restated Investor Rights Agreement]