A Phase 1/2, Multi-center, Open-label, Dose-escalation Study of Elotuzumab(Humanized Anti-CS1 Monoclonal IgG1 Antibody) and Bortezomib in Subjects With Multiple Myeloma Following One to Three Prior Therapies.

Inclusion Criteria

1. Males or females, age 18 years or older.
2. Diagnosis of MM and documentation of 1 to 3 prior therapies.
3. M-protein spike (complete immunoglobulin molecule) of \>= 1g/dL in serum and/or \>= 0.5 g excreted in a 24-hour urine collection sample. Light chain only disease is not an inclusion criteria.
4. Eastern Cooperative Oncology Group (ECOG) performance status 0-2.
5. No prior bortezomib treatment OR responsive (PR or better) to prior bortezomib treatment for a minimum of 3 months OR responsive to prior bortezomib treatment at the time of going to another treatment or ceasing treatment.
6. Alanine aminotransferase (ALT) or aspartate aminotransferase (AST) \<=3 x upper limit of normal (ULN).
7. Total bilirubin \<=2 x ULN.
8. Serum creatinine \<=2.0 mg/dL (unless related to MM, then \<=3.0 mg/dL).
9. Must have adequate bone marrow function defined as:

   * Absolute neutrophil count \>1,000 cells/mm3 (1.0 x 10\^9 cells/L) without growth factor support for 7 days;
   * Platelets \>=75,000 cells/mm3 (75 x 10\^9 cells/L) without transfusion within 72 hours of screening;
   * Hemoglobin \>=8 g/dL without red blood cell transfusion within 2 weeks of screening;
10. Serum calcium (corrected for albumin) level at or below ULN range (treatment of hypercalcemia is allowed and subject may enroll if hypercalcemia returns to normal with standard treatment); additional screening time may be allowed for confirmation - consult with sponsor's medical monitor.
11. Use of appropriate contraception where applicable.
12. Negative urine pregnancy test where applicable.
13. Must have 2-dimensional echocardiogram indicating left ventricular ejection fraction (LVEF) \>=45% within 30 days prior to the first dose of elotuzumab.
14. Ability to understand the purpose and risks of the study and provide signed and dated informed consent and authorization to use protected health information (in accordance with national and local subject privacy regulations).

Exclusion Criteria

1. Life expectancy of less than 3 months.
2. Prior malignancy, except for adequately treated basal cell or squamous cell skin cancer, in situ cervical cancer, or other cancer from which the subject has been disease-free for at least 2 years.
3. Uncontrolled medical problems such as diabetes mellitus, coronary artery disease, hypertension, unstable angina, arrhythmias, pulmonary,(including acute diffuse infiltrative pulmonary and pericardial disease), hepatic, and renal diseases unless renal insufficiency is felt to be secondary to MM.
4. Solitary bone or solitary extramedullary plasmacytoma as the only evidence of plasma cell dyscrasia.
5. Prior treatment with bortezomib in 3 months prior to the first dose.
6. Thalidomide, lenalidomide cytotoxic chemotherapy, or corticosteroids (except prior to infusion of first dose of study drug as prophylaxis for infusion reactions) within 2 weeks of the first dose of elotuzumab.
7. Prior therapy with anti-CD56+ therapeutics.
8. Radiotherapy within 2 weeks prior to the first dose of elotuzumab.
9. Investigational drug within 3 weeks or 3x the half-life of the investigational drug (whichever is longer ) of the first dose of elotuzumab.
10. Prior peripheral stem cell transplant within 12 weeks of the first dose of elotuzumab.
11. Nitrogen mustard agents, melphalan, or monoclonal antibodies within 6 weeks of the first dose of elotuzumab.
12. Neuropathy \>=Grade 2 (NCI CTCAE v3.0).
13. Current orthostatic hypotension.
14. Known active infections requiring antibiotic, antiviral, or antifungal therapy.
15. Serious psychiatric illness, active alcoholism, or drug addiction that may hinder or confuse follow-up evaluation.
16. Any condition that in the investigator's opinion makes the subject unsuitable for study participation.
17. Hypersensitivity to recombinant proteins or excipients in elotuzumab or bortezomib.