A Phase II Study of Belinostat in Combination With Bortezomib in Patients With Relapsed, Refractory Multiple Myeloma

Inclusion Criteria: * Diagnosis of multiple myeloma. * Status of refractory to or relapsed from at least one prior bortezomib-containing regimen. * Progressive disease. * Age \>= 18 years. * Karnofsky performance status \>= 60% * Acceptable liver function: * Bilirubin =\< 1.5 x ULN (upper limit of normal) * Aspartate transaminase (AST) and alanine transaminase (ALT) =\< 3 x ULN * Acceptable hematologic status: * Absolute Neutrophil Count (ANC) \>= 1.5 x 109/L * Platelet count \>= 100 x 109/L * Hemoglobin \>= 9 g/dL * Coagulation status PT-INR/PTT =\< 1.5 x ULN or in the therapeutic range if on anticoagulation therapy. (PT-INR/PTT= prothrombin - international normalized ratio / prothrombin time) * Serum potassium within normal range. * Estimated life expectancy greater than 3 months. * Signed, written IRB (institutional Review Board)-approved informed consent. Exclusion Criteria: * Non-secretory multiple myeloma or symptomatic amyloidosis. * Hypersensitivity to bortezomib, boron, or mannitol. * Less than 4 weeks since prior chemotherapy, radiotherapy, endocrine therapy, or immunotherapy, except if disease is rapidly progressing. * Less than 4 weeks since prior use of other investigational agents. * Serious concomitant systemic disorders (e.g. active infection). * Significant cardiovascular disease. * Marked baseline prolongation of QT/QTc (corrected QT interval)interval. * Central nervous system disorders requiring neuroleptics / anti-convulsants. * Peripheral sensory neuropathy of ≥ Grade 2 * Renal insufficiency defined as a creatinine clearance of \< 30 ml/min. * Non-willingness to use effective contraceptive methods for patients of child-bearing age / potential. * Pregnant or breast-feeding women. * Known HIV positivity. * Prior treatment with belinostat (PXD101), or any other HDAC (histone deacetylase) inhibitor. * Altered mental status which precludes an understanding of the Informed Consent Document.