Safety Study of IgAN, LN, MN, & C3 Glomerulopathy Including Dense Deposit Disease Treated With OMS721

Inclusion Criteria: * At least 18 years of age at screening and competent to provide informed consent; For Cohort 4 only, participants are of Asian descent * Have a diagnosis of one of the following: 1. IgAN on kidney biopsy 2. LN, MN and C3 Glomerulopathy including Dense Deposit Disease on kidney biopsy and 24-hour Urine Protein Excretion (UPE) \> 1000 mg/24 hours (for Cohort 1 only) 3. IgAN diagnosis is confirmed by biopsy within 8 years of screening for Asian descent (for Cohort 4 only) * For Cohort 4 only: subjects with IgAN of Asian descent, documented history of 24-hour UPE \> 1 g within 6 months prior to Screening or Urine Protein-Creatinine Ratio (uPCR) \> 0.75 by spot urine at screening * Screening Estimated Glomerular Filtration Rate (eGFR) \>= 30 mL/min/1.73 m\^2 * Are on physician-directed, stable, optimized treatment with angiotensin converting enzyme inhibitors (ACEI) and/or angiotensin receptor blockers (ARB) and have a systolic blood pressure of \< 150 mmHg and a diastolic blood pressure of \< 90 mmHg at rest Exclusion Criteria: * Have a hemoglobin less than 9.0 g/dL * Have a platelet count =less than 100,000/mm\^3 * Have an absolute neutrophil count \<500 cells/mm\^3 * Have an Alanine aminotransferase (ALT) or Aspartate Aminotransferase (AST) greater than 5.0 x the upper limit of normal (ULN) * Have systemic manifestations of Henoch-Schonlein purpura within 2 years prior to Screening * Have used: belimumab, eculizumab, or rituximab within 6 months prior to Screening * Have a history of renal transplant * History of human immunodeficiency virus (HIV), evidence of immune suppression, active hepatitis C virus (HCV) infection (subjects with positive anti-HCV antibody * Have a malignancy except for adequately treated and cured basal or squamous cell skin cancer, curatively treated in situ disease, or other cancer from which the patient has been disease-free for 5 years or more