The combination of PARP inhibitor (ABT-888) with a proteasome inhibitors (bortezomib) have demonstrated significant anti-myeloma effects in preclinical lab and animal studies. The goal of this phase I trial is to evaluate in patients with relapsed or refractory multiple myeloma the safety, toxicity profile and tolerability of ABT-888 (Veliparib) administered on a schedule including twice daily oral dosing for 14 days followed by 1 week rest in combination with standard dosing of Bortezomib.

This is a dose-finding / dose escalation phase I trial of ABT-888 (Veliparib) in combination with Bortezomib and Dexamethasone in patients with relapsed or refractory multiple myeloma. ABT-888 is given orally (PO) twice daily (every 12 hours) for 14 days in a 21 days cycle.

First dose to be given within 1 hour of Bortezomib on day 1. Planned starting dose is 20 mg PO every 12 hours. Starting dose escalation is planned until an MTD is reached.

Inclusion Criteria:

• Confirmed diagnosis of multiple myeloma.
• Measurable disease, according to the International Myeloma Working Group criteria.
• ECOG performance status 0, 1 or 2.
• Patients must have received prior treatment for MM and have relapsed or progressed on prior therapy; no limit on number of prior treatment regimens, but prior treatment must be completed 2 weeks prior to registration. Prior exposure to Bortezomib is not an exclusion criteria as long as patients did not progress or relapse while receiving or within 3 months of completing trt with bortezomib
• Prior radiation, completed at least 4 weeks prior to registration, is permitted.
• Adequate marrow reserve, liver and renal function

Exclusion Criteria:

• patients with a history of other malignancies, except: adequately treated nonmelanoma skin cancer, curatively treated in-situ cancer of the cervix, prostate cancer with stable PSA for > 3 years, or other solid tumours curatively treated with no evidence of disease for > 5 years.
• Patients with preexisting grade 2 (or higher) sensory neuropathy or grade 1 sensory neuropathy with neuropathic pain.
• Pregnant or lactating women
• Patients receiving concurrent treatment with other anti-cancer therapy any other investigational agents.
• Active or uncontrolled infections
• Patient with known documented congenital or acquired risk factor for thromboembolic event
• Patients with known brain metastases should be excluded from this clinical trial because of their poor prognosis and because they often develop progressive