A Study of TAK-664 in People With Primary Immunodeficiency Diseases Who Have Not Yet Been Treated With Immunoglobulins

Primary immunodeficiency disease (or PIDD) is a group of conditions in which the immune system does not work properly. Some people with PIDD do not make enough antibodies. Antibodies are proteins that help to either protect the body from infections or fight infections. The main type of antibodies that helps protect the body from infection is IgG. People who do not make enough IgG often need medical treatment that gives the body those antibodies. This treatment is called IgG replacement therapy. It can be given through a vein (intravenous or IV) or under the skin (subcutaneous SC). TAK-664 is approved worldwide for SC IG replacement therapy. The study wants to learn more about TAK-664 given to people with PIDD who have not yet been treated with IG (called 'treatment-naïve'). The main aim of the study is to check if giving TAK-664 daily for 5 days, and then once more 3 days later (Day 8), can raise IgG to the target level and keep IgG there. Another aim of the study is to learn if TAK-664 given once a week can keep the IgG at the target levels during the study. The study also wants to find out how much the IgG levels raise and learn how many infections occur and how they are treated.

Inclusion Criteria: 1. The participant or the participant's legally authorized representative is willing and able to understand and fully comply with trial procedures and requirements, in the opinion of the investigator. 2. The participant or the participant's legally authorized representative has provided informed consent or assent, if applicable (that is, in writing, documented via a signed and dated informed consent form \[ICF\]), and any required privacy authorization before the initiation of any trial procedures. 3. The participant is at least 6 years of age at the time of signing the ICF or assent, if applicable. 4. The participant has a documented diagnosis of a form of primary humoral immunodeficiency involving a defect in antibody formation and requiring IG replacement, as defined according to the International Union of Immunological Societies (IUIS) Committee (Human Inborn Errors of Immunity: 2024 update on the phenotypic classification from the IUIS Expert Committee). 5. The participant has never received immunoglobulin (IG) replacement treatment (that is, no prior IG replacement therapy). 6. The participant must have an immunoglobulin G (IgG) level of less than or equal to (\=\] 3 and/or known urinary protein loss greater than \[\>\]1 gram per 24 \[g/24\] hours or nephrotic syndrome), has acute renal failure, is on dialysis, and/or has severe renal impairment on screening laboratory testing (blood urea nitrogen \[BUN\] or creatinine \>2.5 × upper limit of the normal range \[ULN\]). 2. The participant has immunoglobulin A (IgA) deficiency (IgA less than \[\100 millimeters of mercury (mm Hg) and/or systolic blood pressure \>160 mm Hg during the screening period confirmed on 2 measures \>30 minutes apart). 8. The participant has an acquired or inherited thrombophilic disorder, such as protein C deficiency, protein S deficiency, antithrombin deficiency, or primary antiphospholipid antibody syndrome. 9. The participant has malignancies of lymphoid cells, such as chronic lymphocytic leukemia and non-Hodgkin's lymphoma, which may lead to secondary hypogammaglobulinemia. 10. The participant has a medical condition, laboratory finding, or physical examination finding that precludes participation or clinical evidence of any significant acute or chronic disease that, in the opinion of the investigator, may interfere with the successful completion of the trial or place the participant at undue medical risk. 11. The participant has abnormal laboratory values at screening that meet any one of the following criteria (abnormal tests may be repeated once to determine if they are persistent): * Persistent alanine aminotransferase (ALT) and aspartate aminotransferase (AST) \>2.5 × ULN for the testing laboratory. * Persistent severe neutropenia (defined as an absolute neutrophil count (ANC) \1 mg/kg of prednisone-equivalent/day for \>30 days within 3 months of screening. Note: Participants using short-pulse dose corticosteroid course and oral daily corticosteroids \