In this study, researchers will learn more about the use of felzartamab in kidney transplant patients who have antibody-mediated rejection, also known as AMR. Kidney transplants can save lives for people with kidney failure. But even after a successful transplant, the body's immune system can sometimes attack the new kidney. Antibody-mediated rejection (AMR) is when a person's immune system attacks a transplanted organ, like a new kidney. In the person receiving the transplant, their immune system creates specific antibodies. Antibodies are proteins that help the body fight infections. In people with AMR, these antibodies mistakenly see the new organ as a threat and damage its blood vessels. This can cause the new organ to fail. In this study, researchers will learn more about how a study drug called felzartamab affects people with AMR. Felzartamab is a monoclonal antibody, which means it is an antibody made in a laboratory. Felzartamab can target immune cells that produce antibodies, helping to lower their buildup in the kidneys. The main goal of this study is to compare how felzartamab works in participants with kidney transplants who experience AMR compared to a placebo. A placebo is something that looks like the study drug but does not contain any medicine. A placebo is also given in the same way as the study drug. All participants in this study will have active AMR or AMR that has lasted for at least 6 months after their kidney transplant. The main question that researchers want to answer is: • How many participants have biopsy results showing that their transplanted kidney tissue looks normal or near normal after 24 weeks of treatment? Researchers will also learn about: * How long it takes before the participants' disease gets worse * How long the participants' urine protein levels stay low * Kidney biopsy scores to check for blood vessel inflammation at 6 months and 1 year * How many people have no blood vessel inflammation at these times * Changes in donor deoxyribonucleic acid (DNA) levels in blood from the start of treatment * Biopsy test scores for signs of rejection and inflammation at 6 months and 1 year * Changes in kidney function from the start of treatment * How many people have biopsy results showing their kidney tissue looks normal again * How long the transplanted kidney keeps working * How many participants have medical problems during the study * How many participants show signs of another type of kidney transplant rejection called T-cell-mediated rejection (TCMR) at Week 24 and Week 52 * How do results from vital signs, electrocardiograms (ECGs), and blood and urine tests change over time * How felzartamab is processed by the body * How many participants develop antibodies against felzartamab in the blood The study will be done as follows: * Participants will be screened to check if they can join the study. This will take up to 42 days. * There will be 2 parts in this study. * Part A of the study is double blind. This means that neither the participants, study doctor, or site staff know if the participants received the study drug or a placebo. During Part A, participants will be randomized to receive up to 9 doses of either felzartamab or placebo. * Part B of the study is open label. This means that the participants, study doctor, and site staff know which study drug the participant is receiving. During Part B, all participants from Part A will receive up to 9 doses of felzartamab. * All doses will be given through an intravenous infusion. This means it will be given into a vein. The dose the participants receive will depend on their body weight. * Part A will last up to 24 weeks. Part B will last up to 28 weeks. In total, participants will have up to 21 study visits and will be in the study for about 1 year.