This is a prospective, multicenter, open-label, single-arm study to assess the efficacy, safety, and pharmacokinetics (PK) of IgPro20 in adults with hematologic malignancies treated with B-cell targeting Chimeric antigen receptor T-cell (CAR T-cell) and T-cell redirecting therapies (such as T-cell engager bispecific antibody [TCE BsAb] therapy). The primary objective is to demonstrate that true annualized rate of serious bacterial infection (SBIs) is less than (<) 1.0.

This study includes two cohorts:

1. Loading Cohort: Participants with serum immunoglobulin G (IgG) < 500 milligrams per deciliter (mg/dL) at Screening, with or without ongoing immunoglobulin replacement therapy (IgRT) during Screening, who must have received five doses of IgPro20 during the Initial Treatment Period.
2. Maintenance-only Cohort: Participants with serum IgG greater than or equal to (≥) 500 mg/dL and ongoing IgRT at Screening, who must have received one dose of IgPro20 during the Initial Treatment Period.

Inclusion Criteria:

• Participants greater than or equal to (≥) 18 years of age at the time of providing written informed consent.

• Confirmed diagnosis of B-cell hematologic malignancy (ie, Multiple myeloma [MM], Chronic lymphocytic leukemia [CLL], Non-Hodgkin lymphoma [NHL], or BALL) according to applicable diagnostic criteria.

• Participants treated with Chimeric antigen receptor T-cell (CAR T-cell) therapy or TCE BsAb and are:

  1. At least 2 months after receipt of an approved CAR T-cell therapy for the B-cell hematologic malignancy at the time of Screening, or
  2. At least 1 month after initiation of an approved TCE BsAb therapy for the B-cell hematologic malignancy at the time of Screening and expected to continue with the therapy.

• Documented partial or complete response to CAR T-cell or TCE BsAb therapy based on applicable response criteria at the time of Screening:

  1. CLL based on International Workshop on Chronic Lymphocytic Leukemia response criteria
  2. MM based on International Myeloma Working Group response criteria
  3. NHL based on Lugano Classification criteria
  4. B-ALL based on National Comprehensive Cancer Network guidelines

• IgG level (excluding paraprotein, if relevant) at Screening:

If participant has ongoing IgRT (intravenous immunoglobulin [IVIG] or subcutaneous immunoglobulin [SCIG]) for SID during Screening, then any IgG level at Screening is acceptable for enrollment. Participants with IgG less than (<) 500 milligrams per deciliter (mg/dL) are assigned to the Loading Cohort, participants with IgG ≥ 500 mg/dL are assigned to the Maintenance-only Cohort.

• IgG level (excluding paraprotein, if relevant) at Screening:

If participant does not have ongoing IgRT (IVIG for > 8 weeks or SCIG for > 2 weeks) for SID during Screening and are not expected to receive IgRT during Screening, then IgG < 500 mg/dL is required for enrollment (participant is assigned to the Loading Cohort)

Exclusion Criteria:

• Documented history of diseases for which IgRT may be indicated: primary immune deficiency, chronic inflammatory demyelinating polyneuropathy, Guillain-Barré syndrome, immune thrombocytopenia, Kawasaki disease, Lambert-Eaton myasthenic syndrome, multifocal motor neuropathy, myasthenia gravis, stiff person syndrome, solid organ transplant, and rejection prior to Screening.
• History of thromboembolic event (TEE) within 6 months before Screening.
• Eastern Cooperative Oncology Group performance status > 1.
• Presence of any systemic active infection at Screening.
• Participants on any prohibited therapies, including anti-infective treatments.
• Absolute neutrophil count < 1 × 10*9/L (Common Terminology Criteria for Adverse Events [CTCAE] Grade 3 or worse), unless proven to be due to the underlying disease and raised above the limit by granulocyte colony-stimulating factor.
• Concurrent participation in other interventional clinical studies. Note: a participant may be enrolled if their participation in the other study will not jeopardize their safety and / or the scientific validity of this study (eg, an observational study, a long-term safety follow-up of an interventional study, diagnostic device studies, phase 4 studies with medicines used within their approved indication); the investigator may consult with the medical monitor.

CSL will consider on a case-by-case basis requests to share Individual Patient Data (IPD) with external bona-fide, qualified scientific and medical researchers. For information on the process and requirements for submitting a voluntary data sharing request for IPD, please contact CSL at clinicaltrials@cslbehring.com.

Requests for IPD will generally be considered once review by major regulatory authorities (ie FDA, EMA) is complete and the primary publication is available.

Proposed research should seek to answer a previously unanswered important medical or scientific question.

Applicable country specific privacy and other laws and regulations will be considered and may prevent sharing of IPD.

If the request is approved and the researcher has executed an appropriate data sharing agreement, IPD that has been appropriately anonymized will be available.

This is open-label study.