Study of ACY-1215 Alone and in Combination With Bortezomib and Dexamethasone in Multiple Myeloma

Inclusion Criteria: * Patient has relapsed or relapsed/refractory MM with measurable disease parameters according to the International Myeloma Working Group (IMWG) Criteria * Refractory is defined as experiencing less than minimal response (MR) to or progressive disease (PD) within 60 days after completion of the most recent anti-MM regimen * Relapsed is defined as experiencing PD that requires therapy but which is not refractory following the achievement of stable disease (SD) or better to the most recent anti-MM regimen. * Patient received at least 2 prior regimens for MM. * Patient received prior treatment for MM with a proteasome inhibitor and an immunomodulatory drug, unless not a candidate for a proteasome inhibitor or an immunomodulatory drug. * Patient either is not a candidate for autologous stem cell transplant (ASCT), has declined the option of ASCT, or has relapsed after prior ASCT. * Patient is ≥18 years of age. * Patient has a Karnofsky Performance Status score of ≥70 * Patient has adequate bone marrow reserve, as evidenced by: * Absolute neutrophil count (ANC) of ≥1.0x109/L. * Platelet count of ≥ 75x109/L in patients in whom \<50% of bone marrow nucleated cells are plasma cells and ≥50x109/L in patients in whom more than 50% of bone marrow nucleated cells are plasma cells. * Patient has adequate renal function (calculated creatinine clearance of ≥30 mL/min according to the Cockroft-Gault) * Patient has adequate hepatic function (serum bilirubin values \<2.0 mg/dL and ALT and/or AST values \<3 × the upper limit of normal ULN). * Patient has a corrected serum calcium ≤ULN. Exclusion Criteria * Patient has received any of the following therapies: * Radiotherapy or systemic therapy within 2 weeks of baseline * Prior peripheral autologous stem cell transplant within 12 wks of Baseline. * Prior allogeneic stem cell transplant. * Prior treatment with an HDAC inhibitor. * Patient has an active systemic infection requiring treatment. * Patient has a history of other malignancies unless has undergone definitive treatment more than 5 yrs prior to study and without evidence of recurrent malignant disease (excluding basal cell carcinoma of the skin; superficial carcinoma of the bladder; carcinoma of the prostate with a current prostate-specific antigen \<0.1 ng/mL; or cervical intraepithelial neoplasia). * Patient has known or suspected HIV, positive for hepatitis B or is known or suspected to have active hepatitis C infection. * Patient has a history of significant cardiovascular, neurological, endocrine, gastrointestinal, respiratory, or inflammatory illness including recent myocardial infarction (within 6 months)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 a QTcF value of \>480 msec; family or personal history of long QTc syndrome or ventricular arrhythmias including ventricular bigeminy; previous history of drug-induced QTc prolongation * Patient has \> Grade 2 painful neuropathy or peripheral neuropathy * Patient has a history of allergic reaction attributable to bortezomib or other compounds containing boron or mannitol (Phase 1b and 2a only)