Elotuzumab and Lenalidomide After Stem Cell Transplant in Treating Patients With Newly Diagnosed Multiple Myeloma

Inclusion Criteria: * Patients must have undergone autologous stem cell transplantation, within 18 months of initiation of induction therapy for newly diagnosed myeloma * Time to initiation of maintenance therapy: patients may start maintenance therapy as early as 60 days post-transplant and up to 210 days post-transplant; as long as they meet the following criteria: * Platelet count \>= 100,000/mm\^3 * Neutrophil count \>= 1000/mm\^3 (no growth factors within 5 days) * Alanine aminotransferase (ALT) and aspartate aminotransferase (AST) =\< 3 x ULN * Creatinine \< 2.5 mg/dl * Recovered (i.e., =\< grade 1 toxicity) from the reversible effects of autologous stem cell transplant * Patients whose primary therapy was changed due to suboptimal response or toxicity will be eligible, however no more than 2 regimens will be allowed prior to ASCT * Patients must have an Eastern Cooperative Oncology Group (ECOG) status of 0 to 2 * Voluntary written informed consent before performance of any study-related procedure not part of normal medical care, with the understanding that consent may be withdrawn by the subject at any time without prejudice to future medical care * Female patients who: are postmenopausal for at least 24 months before the screening visit, OR; are surgically sterile, OR; if they are of childbearing potential, agree to practice 2 effective methods of contraception, at the same time, 28 days prior to starting study drug, during study treatment and for 28 days after the l…