A Study About the Long-Term Safety of TAK-881 in People With Primary Immunodeficiency Diseases

The study consists of two Epochs: Epoch 1 and Epoch 2. In Epoch 1 eligible participants will have the opportunity to receive TAK-881 for a minimum of 6 months. After 6 months in study TAK-881-3002, the results of the anti-rHuPH20 binding antibody assay from either study TAK-881-3001 (NCT05755035) or study TAK-881-3002 (Epoch 1) will be used to determine the next steps in the study: * Epoch 1: Participants with an anti-rHuPH20 antibody titer less than \[\<\] 1:160 will complete the EOS visit on the day of the first non-investigational product (IP) infusion following Study Visit Week 25. * Epoch 2: Participants with an anti-rHuPH20 antibody titer greater than or equal to \[\>=\] 1:160 at any time point during Study TAK-881-3001 (NCT05755035) and/or study TAK-881-3002 (Epoch 1), will continue with an additional two years of TAK-881 treatment and undergo safety follow-up and will complete the EOS visit on the day of the first non-IP infusion following study Visit Week 121.