Inclusion Criteria: - 18 years of age or older - Must have received prior 1-5 therapies for their myeloma and have relapsed or refractory multiple myeloma. Prior therapy with bortezomib is allowed as long as they were not refractory to bortezomib - Monoclonal protein serum of 1gm/dL or greater or monoclonal light chain in the urine protein electrophoresis of 200 mg/24 hours or greater, or measurable light chains by free light chain assay of 10 mg/dL or greater, or measurable plasmacytoma - ECOG Performance Status 0, 1, or 2 - Laboratory values as outlined in the protocol Exclusion Criteria: - Uncontrolled infection - Cytotoxic chemotherapy < 3 weeks, or biologic or targeted novel therapy < 2 weeks, or corticosteroids < 2 weeks prior to registration. Patients may be receiving chronic corticosteroids if they are being given for disorders other than myeloma - Pregnant women - Nursing women - Men or women of child-bearing potential who are unwilling to employ adequate contraception - Other concurrent chemotherapy, immunotherapy, radiotherapy, or any ancillary therapy considered investigational - Known to be HIV positive - Radiation therapy < 2 weeks prior to registration