The main goal of this study is to show that people with certain immune problems (from Chronic Lymphocytic Leukemia, Multiple Myeloma, or Non-Hodgkin Lymphoma) get fewer serious infections when they receive Gamunex C through an IV once every 4 weeks, along with their usual medical care, for one year.

All participants will receive Gamunex-C 500 mg/kg once every 4 weeks (total 13 doses) starting Day 1 (Week 1) through Week 48 (end of Treatment Phase).

Inclusion Criteria:

Participants with documented and confirmed diagnosis of any of the diseases below:

• B-cell CLL according to iwCLL criteria and Rai staging of intermediate (1 and 2) or high (3 and 4); or
• MM according to the International Myeloma Working Group criteria (IMWG), R ISS stage II or, III; or
• Histologically confirmed diagnosis of B-cell NHL, Stage III or above (IV, Progressive/refractory, or recurrent/relapsed stage) according to the Lugano Classification.

Participants with HGG with IgG levels <5g/L at screening.

Exclusion Criteria:

• Participants with documented history of allogeneic hematopoietic stem cell transplant within 6 months before Screening Visit.
• Participants currently receiving immunoglobulin replacement therapy (IgRT) or have received IgG replacement treatment (i.e., prior immune globulin replacement therapy) within 6 months before the Screening Visit.
• Participants with any active infections at the time of Screening Visit. Participants with active secondary malignancies.
• Participants with known PID.
• Participants with a life expectancy less than 1.5 years.
• Participants with clinical evidence of any significant acute or chronic disease that, in the opinion of the investigator, may interfere with successful completion of the trial or place the participant at undue medical risk.
• Participants who have had known serious treatment related adverse events to immunoglobulin or any anaphylactic reaction to blood or any blood-derived product.
• Participants who have known Selective Immunoglobulin A (IgA) Deficiency (with or without antibodies to IgA) (Note: exclusion is for the specific diagnostic entity. It does not exclude other forms of humoral PI which have decreased IgA in addition to decreased IgG requiring IgG replacement).
• Females of childbearing potential who are pregnant, have a positive pregnancy test at Screening Visit (serum human chorionic gonadotropin-based assay), are breastfeeding, or unwilling to practice a highly effective method of contraception (oral, injectable or implanted hormonal methods of contraception, placement of an intrauterine device or intrauterine system, condom or occlusive cap with spermicidal foam/gel/film/cream/suppository, male sterilization, or true abstinence*) throughout the study. Note: *True abstinence: When this is in line with the preferred and usual lifestyle of the participant. (Periodic abstinence [e.g., calendar, ovulation, symptothermal, post-ovulation methods], declaration of abstinence for the duration of a trial, and withdrawal are not acceptable methods of contraception.)
• Participants with severe known kidney disease (as defined by estimated glomerular filtration rate Chronic Kidney Disease Epidemiology Collaboration [eGFR CKD-EPI] <30 mL/min/1.73 m2) as determined by the Principal Investigator.
• Participants that have liver enzyme levels (alanine aminotransferase [ALT], aspartate aminotransferase [AST], gamma-glutamyl transferase [GGT], or lactate dehydrogenase [LDH]) greater than 3 times the upper limit of normal at the Screening Visit as defined by the testing laboratory.
• Participants who have a history (either 1 episode within the year prior to the Screening Visit or 2 previous episodes over a lifetime) of thromboembolic events [e.g., DVT, PE, ischemic stroke (transient ischemic attack, and any ischemic cerebrovascular accident), myocardial infarction (including unstable angina and ischemic heart disease diagnosed in the last 6 months), retinal artery occlusion, mesenteric ischemia, and peripheral arterial disease (Fontaine III and IV)]*.(Fontaine I: asymptomatic. IIa: mild claudication. IIb: moderate to severe claudication. III: ischemia with rest pain. IV: ulceration or gangrene).
• Participants who currently have a known hyperviscosity syndrome or hypercoagulable states.
• Participants who have clinical signs and symptoms consistent with current hepatitis B virus or hepatitis C virus infection.
• Participants with non-controlled arterial hypertension (i.e., SBP > 160 mmHg and/or DBP > 100 mmHg), and/or HR >100 bpm.
• Participants have known substance or prescription drug abuse within 12 months before the Screening Visit.
• Participants have participated in another clinical trial within 30 days prior to Screening Visit (NOTE: observational studies without investigative treatments [non-interventional] and interventional studies to treat CLL, MM, or NHL are permitted).
• Participants / caregivers are unwilling to comply with any aspect of the protocol for the duration of the study.
• In the opinion of the investigator, participants may have compliance problems with the protocol and the procedures of the protocol.