We Partner 4 Research

Part A: - Chronic immune thrombocytopenia (ITP) (ITP lasting for greater than or equal to ([>=] 12 months) as defined in the protocol - Normal prothrombin time (PT/INR) and activated partial thromboplastin time (aPTT) - No history of a coagulation disorder - Hemoglobin level greater than (>) 10 gram per deciliter (g/dL) (following blood transfusion is acceptable) and normal white blood cell (WBC) and neutrophil counts (elevated WBC/absolute neutrophil count [ANC] attributed to steroid treatment is acceptable) - Eastern Cooperative Oncology Group (ECOG) performance status grade less than or equal to (<=) 2 - Documented vaccinations against encapsulated bacterial pathogens (Neisseria meningitis, including serogroup B meningococcus [where available], Haemophilus influenzae, and Streptococcus pneumoniae) within 5 years of enrollment - Adequate intravenous (IV) access Part B: - Able to comprehend and to give informed consent for Part B - History of ITP and previously treated with at least 1 dose of BIVV009 in Part A - Evidence of treatment efficacy to BIVV009 as defined by a platelet count > 30*10^9/L on at least 1 occasion OR a doubling of the platelet count from baseline - Participants who have completed the 21-week Part A treatment period but have not reached the Part A End of Study (EOS) visit must have evidence of ongoing or recurrent thrombocytopenia during the Part A safety follow-up/washout period as demonstrated by a platelet count less than (<) 50*10^9/L or a >= 50 percent (%) decrease in platelet count over < 1 week

Part A: - Clinically significant medical history or ongoing chronic illness that would jeopardize the safety of the participant or compromise the quality of the data derived from his/her participation in this study - Clinically relevant infection of any kind within the preceding month of enrollment - History of venous or arterial thrombosis within the preceding year of enrollment - Use of aspirin, nonsteroidal anti-inflammatory drugs (NSAIDs), or anticoagulants within 1 week of enrollment - Clinical diagnosis of systemic lupus erythematosus (SLE) or other active autoimmune disorders associated with anti-nuclear antibodies (ANAs) including those that are medically controlled, at Screening (other than ITP) - Secondary immune thrombocytopenia from any cause including lymphoma, chronic lymphocytic leukemia, and drug-induced thrombocytopenia - Positive hepatitis panel (including hepatitis B surface antigen and/or hepatitis C virus antibody) prior to or at Screening - Positive human immunodeficiency virus (HIV) test result prior to or at Screening Part B: - Presence of unacceptable side effects or toxicity associated with BIVV009 (including prior hypersensitivity reactions to BIVV009) such that there is an unfavorable risk-benefit assessment for continued treatment with BIVV009 in the opinion of the Investigator and/or Sponsor - For participants who have completed the 9-week safety follow-up/washout period and final study visit before entry into Part B, a positive hepatitis panel (including hepatitis B surface antigen and/or hepatitis C virus antibody) prior to or at Screening. Patients who have undergone hepatitis C antiviral therapy may be allowed if they are documented to be negative for hepatitis C virus ribonucleic acid (RNA) on at least 2 occasions separated by at least 3 months (including 1 RNA test at least 6 months after completion of antiviral therapy) and are also negative for hepatitis C virus RNA at Screening - Use of prescribed or over-the-counter medications, supplements, vitamins, and/or herbal remedies within 2 weeks before the first dose of BIVV009 in Part B, which in the judgment of the Investigator may adversely affect the participants welfare or the integrity of the study results (excluding hormonal contraception in female participants) - If previously treated with rituximab, the last dose of rituximab was administered < 12 weeks before the first dose of BIVV009 in Part B - Clinical diagnosis of systemic lupus erythematosus (SLE) or other active autoimmune disorders associated with anti-nuclear antibodies (ANA), including those that are medically controlled, at Screening (other than ITP). Positive ANAs at screening that are not associated with an autoimmune disorder (other than ITP) may be allowed if present for >= 28 days without associated clinically relevant symptoms