This study involves taking the study drug, abatacept, by intravenous (IV) infusion. Along with the study drug, participants will take a either cyclosporine or tacrolimus, and methotrexate, which are standard medications for transplant patients. Participants, 6 years of age and older, will be randomized (placed into a group by chance) by the study team. After being placed into a group, you will receive additional doses of either abatacept (the study drug) or a placebo (an inactive substance).