This study is focused on testing the long-term safety of a medicine called TAK-881 in people with Primary Immunodeficiency Diseases (PIDD). PIDD means the immune system doesn't work as well as it should. The study includes people who already took part in a prior study known as TAK-881-3001 and involves getting TAK-881 through an infusion, which is when medicine is slowly put into the body through a tiny tube.

Participants will receive TAK-881 every 2, 3, or 4 weeks, based on doctor recommendations, for at least 6 months. The study is divided into two parts, called Epoch 1 and Epoch 2. People will continue with the study for up to two years based on their body's response. Regular clinic visits every 12 weeks are required to ensure safety and effectiveness.

• Study Duration: Minimum of 6 months, up to 2 years.
• Clinic Visits: Every 12 weeks.
• Eligibility: Completion of prior study TAK-881-3001 is necessary.

The study aims to make sure TAK-881 is safe for long-term use. Participation requires understanding and meeting all eligibility criteria. Participants should not join if they have other serious medical conditions or are involved in other clinical studies.