This phase II trial studies how well elotuzumab works when given with lenalidomide as maintenance therapy after transplant in patients with newly diagnosed multiple myeloma who underwent transplant using their own stem cells (autologous transplant). Maintenance therapy is treatment that is given to help keep cancer from coming back after it has disappeared following the initial treatment. Immunotherapy with monoclonal antibodies, such as elotuzumab, may help the body's immune system attack the cancer, and may interfere with the ability of tumor cells to grow and spread. Biological therapies, such as lenalidomide, may stimulate or suppress the immune system in different ways and stop cancer cells from growing. Adding elotuzumab to standard maintenance therapy with lenalidomide may work better in treating patients with multiple myeloma who have undergone transplant.

PRIMARY OBJECTIVES:

I. Establish activity of elotuzumab and lenalidomide in the maintenance setting post autologous stem cell transplant (ASCT) in myeloma patients.

II. Progression free survival (PFS).

SECONDARY OBJECTIVES:

I. Progression free survival 2. II. Overall survival. III. Determine incidence of secondary primary malignancy. IV. Evaluate the best response rate (stringent complete response [sCR]/very good partial response [VGPR]/partial response [PR]) based on International Myeloma Working Group (IMWG) criteria.

V. Evaluate time to progression. VI. Evaluate time to next therapy. VII. Evaluate the tolerability and toxicity. VIII. Perform MD Anderson Symptom Inventory (MDASI)-Myeloma symptom evaluation.

OUTLINE:

Patients receive elotuzumab intravenously (IV) over 2-4 hours on days 1, 8, 15, and 21 of courses 1-2 and on day 1 of each subsequent course. Patients also receive lenalidomide orally (PO) on days 1-28. Courses repeat every 28 days in the absence of disease progression or unacceptable toxicity.

After completion of study treatment, patients are followed up at 30 days.

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 last dose of study treatment, OR agree to completely abstain from heterosexual intercourse; male patients, even if surgically sterilized (i.e., status post vasectomy), who: agree to practice effective barrier contraception during the entire study treatment period and through 28 days after the last dose of study treatment, OR; agree to completely abstain from heterosexual intercourse

Exclusion Criteria:

• Major surgery within 14 days before the first dose of study drug
• Radiotherapy within 14 days before enrollment
• Known active central nervous system involvement
• Inability to swallow oral medication, inability or unwillingness to comply with the drug administration requirements, or gastrointestinal (GI) procedure that could interfere with the oral absorption or tolerance of treatment
• Female subject is pregnant or lactating
• Known active hepatitis B virus hepatitis, or known active hepatitis C virus
• Infection requiring systemic IV antibiotic therapy within 7 days before cycle 1 day 1 of therapy
• Known allergy to any of the study medications, their analogues, or excipients in the various formulations
• Failure to have fully recovered (i.e., =< grade 1 toxicity) from the effects of prior chemotherapy regardless of the interval since last treatment
• Co-morbid systemic illnesses or other severe concurrent disease that, in the judgment of the investigator, would make the patient inappropriate for entry into this study or interfere significantly with the proper assessment of safety and toxicity of the prescribed regimens