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

Inclusion Criteria: Participants may be included in the study only if they meet all of the following criteria: 1. Have a diagnosis of one of the following: * IgAN diagnosed on kidney biopsy * Lupus nephritis diagnosed on kidney biopsy (Cohort 1 only) * Primary MN diagnosed on kidney biopsy (Cohort 1 only) * C3 glomerulopathy including Dense Deposit Disease diagnosed on kidney biopsy (Cohort 1 only) * Biopsy confirmed diagnosis of IgAN within 8 years of screening (Cohort 4 only). 2. Have 24-hour urine protein \> 1000 mg/24 hours. 3. Are age \>= 18 years at Screening Visit 1 and (for Cohort 4 only) are of Asian descent. 4. Have documented history of 24-hour urine protein \> 1 g within 6 months prior to Screening or Urine Protein Creatinine Ratio (uPCR) \> 0.75 by spot urine at Screening (Cohort 4 only). 5. Have an eGFR \> 30 mL/min/1.73 m\^2 calculated by the Chronic Kidney Disease Epidemiology (CKD-EPI) equation at Screening (Cohort 4). 6. Are on physician-directed, stable, optimized treatment with ACEIs and/or ARBs and have a systolic BP of \< 150 mmHg and a diastolic BP of \< 90 mmHg at rest. 7. If female, are either a) not of childbearing potential (i.e., surgically sterilized or postmenopausal for \> 1 year), b) have a negative pregnancy test at Screening and baseline and if sexually active must agree to use 2 medically reliable forms of contraception throughout the study (all Cohorts) and for at least 12 weeks after the last dose of study drug, including possible extended treatments (Cohort 4), or c) have a medically sterilized male partner. Acceptable methods of contraception include a reliable intrauterine device, hormonal contraception, or a barrier method. 8. If male having heterosexual intercourse, are either a) not of reproductive potential or b) if sexually active must agree to use a medically reliable form of contraception throughout the study (all Cohorts) and for at least 12 weeks after the last dose of study drug, including possible extended treatments (Cohort 4). Acceptable methods of birth control include spermicide in combination with a barrier method, or subject's female partner is willing to use medically acceptable methods of birth control (intrauterine device, hormonal contraception, or a barrier method). Exclusion Criteria: 1. Have a known hypersensitivity to any constituent of the investigational product. 2. Have a hemoglobin \< 9.0 g/dL. 3. Have a platelet count \< 100,000/mm\^3. 4. Have an absolute neutrophil count \< 500 cells/mm\^3. 5. Have an alanine aminotransferase or aspartate aminotransferase \> 5.0 x the upper limit of normal. 6. Have systemic manifestations of Henoch-Schonlein purpura (e.g., joint pain, gastrointestinal bleeding, abdominal pain) within 2 years prior to Screening Visit 1. 7. Have used belimumab, eculizumab, or rituximab within 6 months of Screening Visit 1. 8. Treatment with immunosuppressants (e.g., azathioprine or cyclophosphamide), or cytotoxic drugs, for IgAN within 8 weeks prior to Screening. Treatment with immunosuppressants or cytotoxic drugs for IgAN is not allowed during the Run-In Period. Treatment with immunosuppressants are allowed if such treatment is for indications other than IgAN(Cohort 4 only). 9. Have a history of renal transplant. 10. History of human immunodeficiency virus, evidence of immune suppression, active hepatitis C virus (HCV) infection (participants with positive anti-HCV antibody but a non-detected HCV RNA PCR can enroll), hepatitis B virus (HBV) infection (participants with positive HBsAg are excluded. For participants with isolated positive anti-HBc antibody, HBV DNA test by PCR must be non-detectable to enroll). 11. Have any significant infection requiring antibiotic treatment at Screening Visit 1. 12. 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 subject has been disease-free for \>=5 years. 13. Have an expectation of survival of less than 24 months. 14. If female, are pregnant or breastfeeding. 15. Have received any other investigational drug or device or experimental procedures within 30 days of Screening Visit 1. 16. Are an employee of Omeros, the investigative site, a study staff member, or their immediate family member. 17. Have any condition that the Investigator believes would put the subject at risk from participation. 18. For participants in Cohort 4, have received systemic corticosteroids within 8 weeks prior to Screening. Treatment with systemic corticosteroids is not allowed during the Run-In period.