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

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 (<=) 400 milligrams per deciliter (mg/dL) at screening.
7. If a participant has the potential to become pregnant, they must have a negative pregnancy test at screening and agree to employ a highly effective contraceptive measure throughout the course of the trial and for at least 30 days after the last administration of TAK-664.

Exclusion Criteria:

1. The participant has significant proteinuria (greater 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 [<] 0.07 grams per liter [g/L]) associated with known anti-IgA antibodies and a history of hypersensitivity.
3. The participant has a condition(s) that could alter protein catabolism and/or IgG use (for example, protein-losing enteropathies or nephrotic syndrome).
4. The participant has a known history of a positive result or is positive at screening for one or more of the following: hepatitis B virus surface antigen (HBsAg), polymerase chain reaction (PCR) for hepatitis C virus (HCV), or PCR for human immunodeficiency virus (HIV) Type 1 and Type 2. Note: Cured participants with a history of hepatitis C infection who have a negative PCR test at screening are eligible.
5. The participant has a known history or current diagnosis of thromboembolic episodes, such as deep vein thrombosis, pulmonary embolism, myocardial infarction, ischemic stroke, transient ischemic attack, or peripheral artery disease, within 6 months before screening.

6. The participant has a history of malignancy with less than 2 years of complete remission before screening or active malignancy requiring chemotherapy and/or radiotherapy.

   Note: Participants with adequately treated basal cell or squamous cell carcinoma of the skin, carcinoma in situ of the cervix, or stable prostate cancer not requiring treatment are eligible.

7. The participant has congestive heart failure (New York Heart Association class III/IV), unstable angina, unstable cardiac arrhythmias, or uncontrolled hypertension (defined as diastolic blood pressure >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) <=500 per cubic millimeters [/mm^3]).
12. The participant has anemia that would preclude phlebotomy for laboratory studies, according to standard practice at the site, at the discretion of the investigator.
13. The participant has a known or suspected intolerance or hypersensitivity to compounds closely related to TAK-664 or any of the stated ingredients.
14. The participant has an active infection and is receiving systemic antibiotic therapy for the treatment of infection at the time of screening.

15. The participant is required to take or has taken:

    1. Immunomodulatory/immunosuppressive agents that include but are not limited to specific complement inhibitors, rituximab, neonatal Fc receptor inhibitors (for example, efgartigimod), and chemotherapeutic drugs, within 12 months of screening or 5 times the half-life (t1/2) plus 6 months before screening, whichever is longer.
    2. Long-term systemic corticosteroids defined as a daily dose >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 <=10 milligrams per day (mg/day) prednisone-equivalent are allowed.
16. The participant has received a live-attenuated viral vaccination within 3 months of screening.
17. The participant has known substance or prescription drug abuse within 12 months of screening.
18. The participant is pregnant or breastfeeding at the time of screening or planning to become pregnant during participation in the trial.
19. The participant has a current or relevant history of physical or psychiatric illness or any medical disorder that may require treatment or make the participant unlikely to fully complete the trial or any condition that presents undue risk from the trial intervention or procedures.
20. The participant has participated or is scheduled to participate in another clinical trial involving a trial intervention or investigational device within 30 days before screening and during the trial.
21. The participant is a trial site employee, an immediate family member (for example, spouse, parent, child, or sibling), or is in a dependent relationship with a trial site employee who is involved in the conduct of this trial or may consent under duress.