The study includes a screening phase, a ramp-up phase (if needed), a HYQVIA treatment phase, a TAK-881 treatment phase, and an extension phase. Participants who have been receiving cIGSC or IGIV prior to the study will enter a HYQVIA ramp-up phase, starting 1 to 2 weeks after their last pre-study cIGSC or IGIV dose. Participants already on HYQVIA at the time of screening will proceed directly to the treatment phase. After the TAK-881 dosing phase, participants will move on to the TAK-881 extension phase, with the preference for subsequent infusions in the extension phase to be administered by the participant or caregiver at home.