The purpose of this study is to evaluate the efficacy, safety, pharmacokinetics (PK), and pharmacodynamics (PD) of KP104 in participants with IgAN and C3G. The study will start with enrolling the IgAN cohort. Approximately 42 participants with IgAN will be enrolled in 2 stages: Stage 1 will be used to collect safety, immunogenicity, PK, and PD data to select the optimal biologic dose (OBD) of KP104 for IgAN, as well as to preliminarily explore the effect of KP104 on C3G. Stage 2 will be used to collect safety, immunogenicity, PK, PD, and efficacy data at the OBD dose of KP104 for IgAN and C3G. As soon as the OBD for IgAN is determined, eligible participants with C3G will be enrolled and dosed at the OBD for IgAN for a minimum of 48 weeks for weekly maintenance dosing and a minimum of 47 weeks for biweekly maintenance dosing. Approximately 10 participants with C3G will be enrolled.

Inclusion Criteria:

• Weight of >35 kilograms (kg) at Screening
• Body mass index (BMI) of <35 kilograms per square meter (kg/m^2)
• UPCR >1.0 grams per gram (g/g) by 24-hour urine collection at Screening
• Documented diagnosis and clinical status of IgAN or C3G as follows:

IgAN:

• Diagnosis of IgAN verified by biopsy taken within the past 3 years prior to enrolment.
• On stable regimen of angiotensin converting enzyme or angiotensin blocking agents for 12 weeks and/or sodium-glucose cotransporter-2 (SGLT2) inhibitors for 6 weeks at Screening

C3G:

• Diagnosis of C3G verified by biopsy taken within the past 3 years prior to enrolment.

• On stable regimen of angiotensin converting enzyme or angiotensin blocking agents for 12 weeks and/or SGLT2 inhibitors for 6 weeks at Screening

  • Females of childbearing potential and males must practice effective contraception from Screening until 28 days after the end of study (EOS) visit.
  • Females of childbearing potential must have a negative pregnancy test at Screening and within 1 day prior to dosing of study drug

Exclusion Criteria:

• Any clinically significant, poorly controlled underlying illness other than IgAN or C3G, as determined by the investigator
• Treatment of any infection with IV (within 30 days of Screening) or oral (within 14 days of Screening) antibiotics, antivirals, or antifungals
• History of infections with encapsulated organisms
• History of untreated tuberculosis
• Positive serology for hepatitis C virus (HCV) ribonucleic acid (RNA) or human immunodeficiency virus (HIV) at Screening
• History of bone marrow or stem cell transplantation
• Absolute neutrophil count (ANC) <500 cells per microliter (cells/μL)
• eGFR <30 milliliters per minute per 1.73 square meter (mL/min/1.73 m^2) using the Chronic Kidney Disease Epidemiology Collaboration (CKD-EPI) formula
• Presence of crescent formation in >50 percent (%) of glomeruli assessed on renal biopsy
• Nephrotic syndrome defined as presence of substantial proteinuria (> 3.5 g/24 hours), hypoalbuminemia (< 30 grams per liter [g/L]), and edema/hyperlipidemia. Nephrotic range proteinuria alone is acceptable.
• Rapidly progressive glomerulonephritis, defined as a fall in eGFR of > 30 mL/min/1.73 m^2 within 24 weeks prior to the Screening Visit
• Receiving renal replacement therapy or anticipated to require renal replacement therapy during the duration of the study

NOTE: Other protocol defined Inclusion/Exclusion criteria may apply.