Study to Determine the Maximum Tolerated Dose for the Combination of Pomalidomide, Bortezomib and Low-Dose Dexamethasone in Subjects With Relapsed or Refractory Multiple Myeloma

Inclusion criteria: 1. Must be ≥ 18 years at the time of signing the informed consent form. 2. Subjects must have documented diagnosis of multiple myeloma and have measurable disease (serum M-protein ≥ 0.5 g/dL or urine M-protein ≥ 200 mg/24 hours). 3. Subjects must have had at least 1 but no greater than 4 prior anti-myeloma therapies. 4. Subjects must have received at least 2 consecutive cycles of prior treatment with lenalidomide and must be refractory to their last lenalidomide-containing regimen (either as a single agent or in combination). 5. Subjects must have received at least 2 consecutive cycles of prior treatment with a proteasome inhibitor-containing regimen, but must not be refractory to bortezomib (either as a single agent or in combination). 6. Subjects must have documented progression during or after their last anti-myeloma therapy. 7. Subjects must have an Eastern Cooperative Oncology Group (ECOG) performance status score of 0, 1, or 2. Exclusion criteria: 1. Subjects who are refractory to bortezomib either as single agent or in combination. 2. Subjects with peripheral neuropathy ≥ Grade 2 3. Subjects with non-secretory multiple myeloma 4. Subjects with any of the following laboratory abnormalities: * Absolute neutrophil count (ANC) \< 1,000/µL * Platelet count \< 75,000/µL for subjects in whom \< 50% of bone marrow nucleated cells are plasma cells; or a platelet count \< 30,000/ µL for subjects in whom ≥ 50% of bone marrow nucleated cells are plasma cells * Creatinine Clearance \< 45 mL/min according to Cockcroft-Gault formula * Corrected serum calcium \> 14 mg/dL (\> 3.5 mmol/L) * Hemoglobin \< 8 g/dL (\< 4.9 mmol/L; prior RBC transfusion or recombinant human erythropoietin use is permitted) * Serum glutamic oxaloacetic transaminase (SGOT)/ aspartate aminotransferase (AST) or Transaminase, serum glutamic pyruvic (SGPT)/ alanine aminotransferase (ALT) \> 3.0 x upper limit of normal (ULN) * Serum total bilirubin \> 1.5 x ULN 5. Subjects with prior history of malignancies, other than MM, unless the subject has been free of the disease for ≥ 5 years. Except the following: Basal cell carcinoma of the skin, Squamous cell carcinoma of the skin, Carcinoma in situ of the cervix, Carcinoma in situ of the breast, Incidental histologic finding of prostate cancer (T1a or T1b using the TNM \[tumor, nodes, metastasis\] clinical staging system) or prostate cancer that is curative. 6. Subjects with previous therapy with Pomalidomide 7. Subjects with hypersensitivity to thalidomide, lenalidomide, bortezomib, boron, mannitol, or dexamethasone 8. Subjects with ≥ Grade 3 rash during prior thalidomide or lenalidomide therapy 9. Subjects who had any of the following within the last 14 days of initiation of study treatment: Plasmapheresis, Major surgery (kyphoplasty is not considered major surgery), Radiation therapy, Any anti-myeloma drug therapy 10. Subjects who have received any investigational agents within 28 days or 5 half-lives (whichever is longer) of treatment 11. Pregnant or breastfeeding females 12. Men or women of childbearing potential or their sexual partners who are unwilling to employ adequate contraception. 13. Subjects with known Human immunodeficiency virus (HIV) positivity or active infectious hepatitis A, B, or C