Inclusion Criteria:  Must have received ≥ 2 consecutive cycles of treatment which include an immunomodulatory drug, a proteasome inhibitor, and an anti-CD38 monoclonal antibody either used individually or in combination  Documented refractory or relapsed myeloma  Refractory is defined as progression while on treatment or within 60 days of last treatment  Measurable disease based on at least one of the following lab results within 28 days of enrollment  Serum IgG, IgA, or IgM M-protein ≥ 1.0 g/dL Urine M-protein ≥ 200 mg excreted in a 24-hr collection sample Involved serum free light chain (FLC) ≥ 100 mg/L provided the FLC ratio is abnormal ECOG Performance Status 0 -2 Left Ventricular Ejection Fraction (LVEF) ≥ 55% at rest (MUGA or Echocardiogram) Age ≥ 18 years at the time of consent (Written informed consent and HIPAA authorization for release of personal health information) Females of childbearing potential, and males, must be willing to use an effective method of contraception for the duration of the treatment with study drug plus 90 days (duration of sperm turnover). Eligible for apheresis  Adequate cardiac function as defined as:  No EKG evidence of acute ischemia No EKG evidence of clinically significant conduction system abnormalities in the opinion of the treating investigator No EKG evidence of > Grade 2 (> 480 ms) QTc prolongation No uncontrolled angina or severe ventricular arrhythmias No clinically significant pericardial disease No history of myocardial infarction (MI) in the last 6 months No Class 3 or higher New York Heart Association Congestive Heart Failure  Demonstrate adequate organ function as defined below; all screening labs should be performed within 14 days prior to enrollment.  Absolute lymphocyte count ≥ 400/mm3 Absolute neutrophil count ≥ 1,000/mm3 Platelets ≥ 75,000/mm3 Calculated Creatinine Clearance ≥ 30 ml/min Serum total bilirubin ≤ 1.5 x upper limit of normal AST and ALT < 2.5 times normal  Exclusion Criteria:  Known hypersensitivity to elotuzumab (Elo) Amyloidosis, Waldenstrom's macroglobulinemia, POEMS syndrome, or known central nervous system (CNS) involvement  Receiving chronic systemic steroid therapy or any other form of immunosuppressive therapy within 7 days prior to enrollment.  NOTE: Replacement therapy (eg., thyroxine, insulin, or physiologic corticosteroid replacement therapy for adrenal or pituitary insufficiency, etc.) is not considered a form of systemic treatment. Active autoimmune disease that has required systemic treatment in the past 2 years before enrollment (i.e. with use of disease modifying agents, corticosteroids or immunosuppressive drugs). Serious non-healing wound, ulcer, bone fracture, major surgical procedure, open biopsy or significant traumatic injury within 28 days prior to enrollment Active liver disease (such as cirrhosis, chronic active hepatitis or chronic persistent hepatitis) HIV positive or known active Hepatitis C (e.g., HCV RNA [qualitative] is detected) or Hepatitis B (e.g. HBsAg reactive) virus Active bleeding or a pathological condition that is associated with a high risk of bleeding (therapeutic anticoagulation is allowed) Has an active infection requiring systemic therapy History of active TB (Bacillus Tuberculosis) Has received a live vaccine within 30 days of enrollment. Anti-myeloma drug therapy (including radiation therapy) ≤ 14 days prior to apheresis History of myocardial infarction (within 6 months of enrollment), stable or unstable angina  History of another malignancy within the past 3 years before enrollment. -- Exceptions include:  Basal cell carcinoma of the skin or squamous cell carcinoma of the skin, In situ cancers that have undergone potentially curative therapy Prisoners or patients who are incarcerated Patients who are compulsorily detained for treatment of either a psychiatric or physical illness Pregnant or breastfeeding females: Females of childbearing potential must have a negative pregnancy test within 7 days prior to enrollment.