A Study Evaluating ABT-199 in Multiple Myeloma Subjects Who Are Receiving Bortezomib and Dexamethasone as Standard Therapy

* Eastern Cooperative Oncology Group (ECOG) performance score less than or equal to 1 * Diagnosis of multiple myeloma previously treated with at least 1 prior line of therapy (dose escalation only) or (safety expansion only) received treatment with a proteasome inhibitor or an IMiD(r) or immunomodulatory agent (e.g., thalidomide, lenalidomide). Induction therapy and following stem cell transplant are considered a single line of therapy. * Measurable disease at Screening: Serum monoclonal protein greater than or equal to 1 g/dL by protein electrophoresis, or greater than or equal to 200 mg monoclonal protein in the urine on 24-hr electrophoresis, or serum immunoglobulin free light chain greater than or equal to 10 mg/dL and abnormal serum immunoglobulin kappa to lambda free light chain ratio. * Subjects with a history of autologous or allogenic stem cell transplant must have adequate bone marrow independent of any growth factor support, and have recovered from any transplant related toxicity(s); and either greater than 100 days post-autologous transplant (prior to first dose of study drug) or greater than or equal to 6 months post-allogenic transplant (prior to first dose of study drug) and not have active graft-versus-host disease (i.e., requiring treatment). * Subject must have adequate coagulation, renal, and hepatic function, per laboratory reference range at Screening.

* Exhibits evidence of other clinically significant uncontrolled condition(s), including, but not limited to: uncontrolled systemic infection (viral, bacterial, or fungal), diagnosis of fever and neutropenia within 1 week prior to first dose of study drug * Cardiovascular disability status of New York Heart Association Class greater than or equal to 2. Class 2 is defined as cardiac disease in which patients are comfortable at rest but ordinary physical activity results in fatigue, palpitations, dyspnea or anginal pain. * Significant history of renal, neurologic, psychiatric, endocrinologic, metabolic, immunologic, cardiovascular, pulmonary or hepatic disease, that in the opinion of the investigator, would adversely affect his/her participation in the study. * History of other active malignancies other than multiple myeloma within the past 3 years prior to study entry, with the following exceptions: adequately treated in situ carcinoma of the cervix uteri, basal cell carcinoma of the skin or localized squamous cell carcinoma of the skin, previous malignancy confined and surgically resected (or treated with other modalities) with curative intent. * Tested positive for HIV or hepatitis.