Study to Monitor Subcutaneous Human Immunoglobulin Administered at Modified Dosing Regimens in Patients With Primary Immunodeficiency Diseases

Inclusion Criteria: 1. Age ≥2 years and ≤75 years. 2. Confirmed diagnosis of primary immunodeficiency (PI) disease as defined by the European Society for Immunodeficiencies and Pan American Group for Immunodeficiency and requiring immunoglobulin replacement therapy due to hypogammaglobulinaemia or agammaglobulinaemia. Note: The exact type of PI disease will be recorded. 3. Established on a consistent or stable mg/kg dose of any SCIG treatment for a minimum of 3 months prior to Screening. Note: patients entering Cohort 3 must be on weekly SCIG infusions for a minimum of 12 weeks. 4. Availability of the Immunoglobulin G (IgG) trough levels of 2 previous SCIG infusions within 1 year of Screening, with 1 trough level obtained within 3 months prior to enrollment, and maintenance of trough serum IgG levels ≥5.0 g/L in 2 previous infusions. Patients with no prior IgG trough level within 3 months prior to enrollment may use the Screening IgG trough level as their 2nd reading. 5. Voluntarily given, fully informed signed informed consent. For patients under the legal age of consent, voluntarily given, fully-informed, signed informed consent will be provided by patient's parent or legal guardian, and assent will be provided by patient (per age-appropriate Institutional Review Board \[IRB\] requirements). 6. Females of childbearing potential, who are not nursing and have no plans for pregnancy during the course of the study, have been using at least 1 acceptable form of birth control for a minimum of 30 days prior to the Screening visit and must agree to use at least 1 acceptable method of contraception for 30 days after the last dose of CUTAQUIG. Acceptable methods include: intrauterine device (IUD), hormonal contraception, male or female condom, spermicide gel, diaphragm, sponge, cervical cap, or abstinence. 7. For female patients of child-bearing potential, a negative result in a urine pregnancy test conducted at the Screening visit. 8. Willingness to comply with all aspects of the protocol, including blood sampling, for the duration of the study. Exclusion Criteria: 1. Evidence of active infection within 4 weeks of Screening or during the Screening Period. 2. Current or clinically-significant history of any cardiovascular, respiratory, hepatic, renal, gastrointestinal, endocrine, neurological, immunological (excluding PI), hematologic, and/or psychiatric disorder(s), or a history of any other illness that, in the opinion of the Investigator, might confound the results of the study, or pose additional risk to the patient by participation in the study. 3. Known history of adverse reactions to immunoglobulin A (IgA) in other products. 4. Body mass index (BMI) \>40 kg/m2 for patients entering Cohort 2 or Cohort 3. There are no BMI restrictions for Cohort 1. 5. Ongoing history of hypersensitivity or persistent reactions to blood or plasma derived products, or any component of the investigational product (such as Polysorbate 80). 6. Requirement of any routine premedication for IgG administration. 7. History of malignancies of lymphoid cells and immunodeficiency with lymphoma. 8. Severe liver function impairment (aspartate aminotransferase \[AST\] or alanine aminotransferase \[ALT\] \>3 times above upper limit of normal). 9. Known protein-losing enteropathies or clinically significant proteinuria. 10. Presence of renal function impairment (creatine \>120 μM/L or creatinine \>1.35 mg/dL), or predisposition for acute renal failure (eg, any degree of preexisting renal insufficiency or routine treatment with known nephritic drugs). 11. Treatment with oral or parenteral steroids for ≥30 days, or when given intermittently or as bolus at daily doses ≥0.15 mg/kg when taken within 30 days of Screening. Note: Short or intermittent courses of steroids (ie, a steroid burst) of \>0.15 mg/kg/day is allowed for treatment of a short-term condition such as an asthma exacerbation. 12. Treatment with immunosuppressive or immunomodulatory drugs (except Omalizumab). 13. Use of HYQVIA (Immune Globulin Infusion 10% \[Human\] with Recombinant Human Hyaluronidase) within 3 months prior to first CUTAQUIG infusion. 14. Live viral vaccination (such as measles, rubella, mumps, and varicella) within 2 months prior to first CUTAQUIG infusion. 15. Exposure to blood or any blood product or derivative, other than subcutaneous IgG used for regular PI disease treatment, within 3 months before the first CUTAQUIG infusion. 16. Treatment with any investigational medicinal product within 3 months prior to first CUTAQUIG infusion. Note: Patients participating in Study SCGAM-03 will be allowed to enter this study without the 3-month waiting period for an Investigational Product. Patients receiving another SCIG product within 3 months prior to the first CUTAQUIG infusion may be considered for enrollment after Sponsor approval. 17. Presence of any condition that is likely to interfere with the evaluation of CUTAQUIG or satisfactory conduct of the trial. 18. Known or suspected to abuse alcohol, drugs, psychotropic agents, or other chemicals within the past 12 months prior to first CUTAQUIG infusion. 19. Known active or chronic hepatitis B, hepatitis C, or HIV infection. Past hepatitis B or hepatitis C infection that has been cured is allowed.