The purpose of this study is to evaluate the safety and tolerability and to establish the maximum tolerated dose of JNJ-26481585 combined with VELCADE and dexamethasone.

This is an open-label (patient and study personnel will know what treatment is being administered), multicenter, dose escalation study. Increasing doses of JNJ-26481585 will be explored in combination with the standard VELCADE/dexamethasone dose. After the maximum tolerated dose (MTD) is determined, up to 24 patients will be entered in a treatment group to receive the MTD (and if deemed necessary a lower dose level) to further assess the safety and activity of this combination. There will be 3 phases in the study: a Screening Phase (from signing of informed consent until immediately before dosing), an open-label Treatment Phase (from the first dose of JNJ-26481585 and VELCADE-dexamethasone until the End of Treatment Visit), and a Posttreatment/Follow-up Phase. Patients who achieve a positive response to treatment at the end of Cycle 1 will continue to receive JNJ-26481585 and VELCADE-dexamethasone for a maximum of 11 cycles (eight 3-week treatment cycles, followed by three 5-week treatment cycles). Patients with progressive disease (PD) or unacceptable toxicity will be withdrawn from treatment. In the Follow-Up Phase, patients whose disease has not progressed or who discontinued treatment for reasons other than PD will be assessed approximately every 6 weeks until PD is recorded or until the start of subsequent therapy. The study will end when all patients have been assessed with PD, or 12 months after the last patient is enrolled, whichever is earlier. Patient safety will be monitored. Drug A, JNJ-26481585, will be taken orally on Days 1, 3, and 5 of each week at doses starting at 6 mg and escalating to 12 mg. Drug B, VELCADE, will be given by subcutaneous injection (under the skin) at a dose of 1.3 mg/m2 on Days 1, 4, 8, and 11 of each 21-day cycle (Cycles 1 to 8) and on Days 1, 8, 15, and 22 of each 35-day cycle (Cycles 9-11). Drug C, dexamethasone, will be taken orally on the day of and after VELCADE at a dose of 20 mg. Dosing may be adjusted, based on tolerability.

Inclusion Criteria:

• Eastern Cooperative Oncology Group (ECOG) Performance status score 0-2
• Measurable or secretory multiple myeloma
• Relapse or progression of myeloma following prior systemic antineoplastic therapy
• Pretreatment clinical laboratory values meeting protocol-specified criteria
• Left ventricular ejection fraction rate within normal limits

Exclusion Criteria:

• Peripheral neuropathy or neuralgia >=2, according to National Cancer Institute Common Terminology Criteria for Adverse Events (NCI-CTCAE) version 4.0
• Diagnosis of primary amyloidosis, plasma cell leukemia, or other similar conditions
• Diagnosis of Waldenstrom macroglobulinemia with protocol-specified immunoglobulin levels
• Prior histone-deacetylase inhibitor therapy - More than 3 prior lines of therapy
• Cardiac risk factors: unstable angina or myocardial infarction within the preceding 12 months, congestive heart failure (New York Heart Association Class II-IV), known presence of dilated, hypertrophic, or restrictive cardiomyopathy
• Any other cardiac abnormality that, in the opinion of the investigator, medical monitor, or consultant cardiologist, may place the patient at an unacceptably increased risk with study drug
• History of any of the following: sustained ventricular tachycardia, ventricular fibrillation, Torsades de Pointes, atrial fibrillation, cardiac arrest, Mobitz II second degree heart block, or third degree heart block - QTc at Screening > 450 ms in males / > 470 ms in females
• Family history of short QT syndrome, long QT syndrome
• Obligate use of a cardiac pacemaker - Use of medications that may cause Torsades de Pointes