For more information regarding BMS clinical trial participation, please visit www.BMSStudyConnect.com Inclusion Criteria: - Have received at least 3 prior lines of therapy, including a proteasome inhibitor [PI] and an immunomodulatory agent [IMiD] OR have disease that is double refractory to a PI and IMiD - More than 12 weeks post-transplant of your own blood forming stem cells (autologous transplant) - Have detectable disease measured by a specific protein in your blood and/or urine - Must consent to bone marrow aspirate or biopsy. Exclusion Criteria: - Solitary bone or extramedullary plasmacytoma as the only evidence of plasma cell dyscrasia, or monoclonal gammopathy of undetermined significance (MGUS), smoldering multiple myeloma (SMM), primary amyloidosis, Waldenstrom's macroglobulinemia, POEMS syndrome or active plasma cell leukemia - Prior therapy with anti-PD-1, anti-PD-L1, anti-PD-L2, anti-CD137, anti CTLA 4, or anti-CD38 antibody, or allogeneic stem cell transplantation - Seropositive for human immunodeficiency virus (HIV), Hepatitis B surface antigen or Hepatitis C antibody positive (except if HCV-RNA negative), or history of active chronic hepatitis B or C - History of central nervous system involvement or symptoms suggestive of central nervous system involvement by multiple myeloma Other protocol defined inclusion/exclusion criteria could apply