Inclusion Criteria:  Patients with relapsed or refractory multiple myeloma, as defined by the international myeloma working group (IMWG) updated criteria (Appendix A) who have measurable disease defined by one or more of the following:  Serum myeloma (M)-protein greater than or equal to 0.5 g/dL (5 g/L). Urine M-protein greater or equal to 200 mg/24 h. Involved light chain (either kappa or lambda) is >10 mg/dL with an abnormal kappa: lambda ratio. A biopsy proven plasmacytoma(s) that is new or definitely increased. Increase is defined as a 50% and at least 1 cm increase as measured serially by the sum of the products of the cross-diameters of the measurable lesion. Patients must have received at least 3 prior lines of therapy and have been previously exposed to a proteasome inhibitor, an IMiD and be considered refractory to an FDAapproved anti-CD38 mAb used either in combination or as a single agent. Refractory is defined as progression on or within 60 days of receiving a treatment program containing an anti-CD38 monoclonal antibody. Female or male patients age ≥18 years. Eastern Cooperative Oncology Group (ECOG) Performance Status (PS) 0-2. PS-3 is permitted if PS is due solely to bone pain.  Adequate hematological function including:  Absolute neutrophil count (ANC) >1,000/mm^3 (unless myelosuppression is secondary to bone marrow plasmacytosis expressed by >50% of cellularity). Platelet count >75,000/mm^3 for the dose finding portion, and > 50,000/ mm^3 for the expansion part.(transfusion is not permitted within 7 days of enrollment) Hemoglobin ≥8.0 g/dL (transfusion support is not permitted within 7 days of enrollment).  Adequate Renal Function defined by:  a. Estimated creatinine clearance >30 mL/min as calculated using the CKD-EPI equation. (If an estimated creatinine clearance CrCl is believed to be inaccurate for a patient, 24-hour urine collection with actual assessment of CrCl is allowed)  Adequate Liver Function, including:  Aspartate and alanine aminotransferase (AST and ALT) < 2.5 x upper limit of normal (ULN); <5.0 x ULN if there is liver involvement by the tumor. Alkaline phosphatase <2.5 x ULN (<5 x ULN in case of bone metastasis). Total bilirubin < 2.0 mg/dL, except in patients with Gilbert Syndrome who must have a total bilirubin less than 3.0 mg/dL. Seronegative for Hepatitis B surface (HBs) or Hepatitis B core (HBc) antigens. Patients with positive antigens must be tested for hepatitis B virus (HBV) by reverse transcription polymerase chain reaction (RT-PCR). Patients who are HBV RNA negative are eligible. Seronegative for hepatitis C antibody. If hepatitis C antibody test is positive, patients must be tested for the presence of antigen by RT-PCR. Patients who are hepatitis C virus (HCV) RNA negative with adequate liver function as described above are eligible. Resolved acute effects of any prior therapy to baseline severity or CTCAE Grade ≤ 1, with the exception of peripheral neuropathy attributable to bortezomib.  Serum pregnancy test (for females of childbearing potential) negative at screening. Female patients of non-childbearing potential must meet at least 1 of the following criteria:  Achieved postmenopausal status, defined as follows: cessation of regular menses for at least 12 consecutive months with no alternative pathological or physiological cause; status may be confirmed with a serum follicle stimulating hormone (FSH) level confirming the postmenopausal state. Have undergone a documented hysterectomy and/or bilateral oophorectomy. Have medically confirmed ovarian failure. All other female patients (including female patients with tubal ligations) are considered to be of childbearing potential. Signed and dated Informed Consent by study participant and/ or Legally Authorized Representative (LAR). Willing and able to comply with scheduled visits, treatment plan, laboratory tests, and other procedures.  Exclusion Criteria:  Patients with other malignancies in addition to multiple myeloma are not eligible if the other malignancy has required treatment within the past 3 years or is not in complete remission with the exceptions of successfully treated non-metastatic basal cell carcinoma, squamous cell skin carcinoma, or in-situ carcinoma. History of active autoimmune disorders (including but not limited to: Crohn's disease, rheumatoid arthritis, scleroderma, systemic lupus erythematosus, Grave's disease) and other conditions that require systemic therapy, which may compromise or impair the immune system. Any form of primary immunodeficiency (such as Severe Combined Immunodeficiency Disease). Patients with active uncontrolled bacterial, fungal or viral infection, including known human immunodeficiency virus (HIV) infection or acquired immunodeficiency syndrome (AIDS) related illness. Major surgery within 4 weeks prior to study entry. Radiation therapy within 2 weeks prior to study entry (bone lesions requiring radiation may be treated with limited [i.e., ≤ 25% of bone marrow in field] radiation therapy during this period). Patients with a history of stem cell transplant (autologous or allogeneic) within 100 days prior to study enrollment. Donor Lymphocyte Infusion (DLI) within 30 days prior to study entry. Time between the last doses of previous systemic anti-cancer therapy is less than 5 times the elimination half-life of previous therapy or less than 30 days after last dose of elotuzumab or other Signaling lymphocytic activation molecule F7 (SLAMF7) receptor (also known as anti-CD319) therapy. Recent anti-CD38 therapy is not exclusionary. Patient known to be refractory to platelet or red blood cell transfusions. Any of the following in the previous 6 months: myocardial infarction, severe/unstable angina, coronary/peripheral artery bypass graft, symptomatic congestive heart failure (CHF, New York Heart Association Class III or IV), cerebrovascular accident, transient ischemic attack or symptomatic pulmonary embolism. Patients with a history of cardiac events, and a left ventricular ejection fraction (LVEF) of ≤ 45% at screening will be excluded. Fertile male patients and female patients of childbearing potential who are unwilling or unable to use a highly effective method of contraception as outlined in this protocol for the duration of the study and for at least 28 days after the last dose of investigational product. Other acute or chronic medical or psychiatric condition, including recent (within the past year) or active suicidal ideation or behavior or laboratory abnormality that may increase the risk associated with study participation or investigational product administration or may interfere with the interpretation of study results and, in the judgment of the investigator, would make the patient inappropriate for entry into this study.