The expanded access program allows people to gain access to an unlicensed treatment on compassionate grounds. This study will provide access to TAK-881 for participants with PIDD who have completed study TAK-881-3002 [NCT06076642], who continue to derive clinical benefit from maintenance treatment with TAK-881 and wish to continue this treatment.

All participants will receive TAK-881 as subcutaneous (SC) injection using a qualified medical device (Koru 24 G HIgH Flo Subcutaneous Safety Needle Set) that will be individualized for each participant, at the treating physician's discretion and dependent on serum IgG trough level and clinical response.

Participants will continue treatment until the benefit-risk no longer favors the participant or TAK-881 becomes commercially available in the United States (U.S.), the participant chooses to discontinue treatment, or the program is discontinued by the sponsor.

Inclusion Criteria:

1. Participant has PIDD and has completed the end-of-study visit of Study TAK-881-3002.
2. Participant is demonstrating continued benefit from TAK-881 for the treatment of PIDD in the opinion of the treating physician.
3. Participant, or (in the case of minors) legally designated representative(s) is/are informed of the nature of the expanded access program and can provide written informed consent/assent (if applicable), including providing consent/assent for use of the investigational medical device, before initiation of any program procedures.
4. Participant does not have any condition, including laboratory test result, that in the opinion of the treating physician may compromise the participant's safety.
5. Participant does not have a known hypersensitivity to TAK-881 or its components.

Exclusion Criteria:

1. Participant has potential to become pregnant and the participant does not agree to employ a highly effective form of contraception for the duration of the program.
2. Participant is pregnant or lactating or intends to become pregnant or begin lactating during the program.