Inclusion Criteria:
* All laboratory assessments should be performed within 21 days of initiation of protocol therapy unless otherwise specified.
* Participant has given voluntary signed written informed consent before performance of any study-related procedure that is not part of normal medical care, with the understanding that consent may be withdrawn by the subject at any time without prejudice to their future medical care.
* Eastern Cooperative Oncology Group (ECOG) performance status ≤ 2 (see Appendix A).
* Age ≥ 18 years
* Measurable disease of multiple myeloma as defined by at least one of the following
* Serum monoclonal protein ≥ 0.5 g/dL
* ≥ 200 mg of monoclonal protein in the urine on 24 hour electrophoresis
* Serum free light chain ≥ 100 mg/L (10 mg/dL) and abnormal serum free kappa to serum free kappa light chain ratio
* Previously treated relapsed and refractory multiple myeloma
* Patients must have received at least one prior therapy with at least 2 cycles of lenalidomide and at least 2 cycles of a proteasome inhibitor (either in separate regimens or within the same regimen)
* Disease progression on or within 60 days of completion of last therapy.
* ANC ≥ 1000/μL. G-CSF is not permitted within 14 days of screening.
* Platelet count ≥ 50,000/µL. Platelet transfusion is not permitted within 7 days of screening.
* Hemoglobin ≥ 8 g/dL. Red blood cell transfusions are permitted to meet eligibility criteria.
* Calculated creatinine clearance of ≥ 30 mL/min according to Cockcroft-Gault equation
* Patent has adequate hepatic function, as evidenced by serum bilirubin values \< 2 mg/dL and serum aspartate transaminase (ALT) and/or aspartate transaminase (AST) values \< 3 × the upper limit of normal (ULN) of the local laboratory reference range. Patients with elevated bilirubin due to Gilbert's syndrome may be permitted with PI approval.
* Must be able to take acetylsalicylic acid (ASA) daily as prophylactic anticoagulation. Patients intolerant to ASA may use low molecular weight heparin or equivalent. Warfarin will be allowed provided patient is full anticoagulated, with an INR of 2-3.
* All study participants must be registered into the mandatory POMALYST REMS program, and be willing and able to comply with the requirements of the POMALYST REMS program.
* Able to swallow capsules whole (pomalidomide capsules cannot be crushed, dissolved or broken).
Exclusion Criteria:
* Prior therapy with elotuzumab
* Participants who have had chemotherapy or radiotherapy within 2 weeks (6 weeks for nitrosoureas or mitomycin C) prior to entering the study or those who have not recovered from adverse events due to agents administered more than 2 weeks earlier. Patients may have received dexamethasone within 2 weeks prior to entering study.
* Participants who are receiving any other investigational agents.
* Concomitant high dose corticosteroids except patients may be on chronic steroids (maximum dose 10 mg/day prednisone equivalent) if they are being given for disorders other than myeloma, e.g. adrenal insufficiency, rheumatoid arthritis, etc.
* Pregnant or lactating females
* Prior history of malignancies, other than MM, unless the patient has been free of the disease for ≥ 3 years. Exceptions include the following:
* Basal or squamous cell carcinoma of the skin
* Carcinoma in situ of the cervix
* Ductal carcinoma in situ of the breast
* Incidental histologic finding of prostate cancer (T1a or T1b)
* Another malignancy undergoing active treatment with the exception of non-melanoma skin cancer or in situ cervical cancer.
* Patients with plasma cell leukemia, POEMS syndrome, or amyloidosis are excluded from this trial.
* HIV infection
* Active hepatitis B infection or active hepatitis C infection. Participants who have prior hepatitis C infection but who have received an antiviral treatment and show no detectable viral RNA for 6 months are eligible.
* Peripheral neuropathy ≥ grade 2 despite supportive therapy.
* Hypersensitivity to thalidomide, lenalidomide, pomalidomide, bortezomib, or dexamethasone (such as Stevens-Johnson syndrome). Rash to immunomodulatory drug that can be medically managed is allowable.
* Allogeneic stem cell transplant less than 12 months prior to initiation of study treatment and who have not discontinued immunosuppressive treatment for at least four weeks prior to initiation of study treatment and who are currently dependent on such treatment. Patients may also not have active graft v. host disease.
* Patient has a history of significant cardiovascular, neurological, endocrine, gastrointestinal, respiratory, or inflammatory illness that could preclude study participation, pose an undue medical hazard, or interfere with the interpretation of the study results, including, but not limited to, patients with congestive heart failure (New York Heart Association \[NYHA\] Class 3 or 4); unstable angina; cardiac arrhythmia; recent (within the preceding 6 months) myocardial infarction or stroke; hypertension requiring \> 2 medications for adequate control; diabetes mellitus with \> 2 episodes of ketoacidosis in the preceding 12 months; or chronic obstructive pulmonary disease (COPD) requiring \> 2 hospitalizations in the preceding 12 months.
* Patient has any other medical, psychiatric, or social condition that would preclude participation in the study, pose an undue medical hazard, interfere with the conduct of the study, or interfere with interpretation of the study results
