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

Inclusion Criteria:

* Eastern Cooperative Oncology Group (ECOG) performance score ≤ 2
* Participant has documented relapsed or progressive multiple myeloma on or after any regimen or who are refractory to the most recent line of therapy. Relapsed myeloma is defined as previously treated myeloma that progresses and requires initiation of salvage therapy, but does not meet the criteria for refractory myeloma. Refractory myeloma is defined as disease that is nonresponsive (failure to achieve minimal response or development of progressive disease \[PD\]) while on primary or salvage therapy, or progresses within 60 days of last therapy.
* Participant must have received prior treatment with at least one, but no more than three, prior lines of therapy for multiple myeloma. A line of therapy consists of ≥ 1 complete cycle of a single agent, a regimen consisting of combination of several drugs, or a planned sequential therapy of various regimens.
* Prior treatment with bortezomib or other proteasome inhibitor is allowed, provided ALL of the following criteria are met: Disease is NOT refractory to any proteasome inhibitor, defined as no disease progression (i.e., PD, per International Myeloma Working Group \[IMWG\] or European Society for Blood and Marrow Transplantation \[EBMT\] criteria) while receiving proteasome inhibitor therapy or within 60 days after the last dose, AND best response achieved with any proteasome inhibitor therapy (alone or in combination) was at least a Partial Response (PR), AND participant did not discontinue any proteasome inhibitor due to intolerance or ≥ Grade 3 related toxicity.
* Participant has measurable disease at Screening, defined as at least one of the following: Serum M-protein ≥ 0.5 g/dL, OR Urine M-protein ≥ 200 mg in 24-hours, OR serum immunoglobulin free light chain (FLC) ≥ 10 mg/dL provided serum FLC ratio is abnormal.

Exclusion Criteria:

* Participant is refractory to any proteasome inhibitor, defined as progression on or within 60 days of the last dose of a proteasome inhibitor-containing regimen.
* Participant has had prior treatment with proteasome inhibitor within 60 days prior to first dose of study drug.
* Participant has any of the following conditions:

Non-secretory multiple myeloma, active plasma cell leukemia i.e., either 20% of peripheral white blood cells or greater than 2.0 X 10\^9/liter (L) circulating plasma cells by standard differential, Waldenstrom's macroglobulinemia, amyloidosis, POEMS syndrome (polyneuropathy, organomegaly, endocrinopathy, monoclonal protein, and skin changes), known Human Immunodeficiency Viral (HIV) infection, active hepatitis B or C infection based on blood screen tests, significant cardiovascular disease, including uncontrolled angina, severe or uncontrolled arrhythmia, recent myocardial infarction within 6 months of randomization, or congestive heart failure New York Heart Association (NYHA) Class ≥ 3, major surgery within 4 weeks prior to randomization, acute infections requiring parenteral therapy (antibiotic, antifungal, or antiviral) within 14 days prior to randomization, peripheral neuropathy ≥ Grade 3 or ≥ Grade 2 with pain within 2 weeks prior to randomization, uncontrolled diabetes or uncontrolled hypertension within 14 days prior to randomization, any other medical condition that, in the opinion of the Investigator, would adversely affect the participant's participation in the study

* Participant has a history of other active malignancies, including myelodysplastic syndrome (MDS), within the past 3 years prior to study entry, with the following exceptions: Adequately treated in situ carcinoma of the cervix uteri or the breast, basal cell carcinoma of the skin or localized squamous cell carcinoma of the skin, prostate cancer Gleason grade 6 or lower AND with stable Prostate Specific Antigen (PSA) levels off treatment, previous malignancy with no evidence of disease confined and surgically resected (or treated with other modalities) with curative intent and unlikely to impact survival during the duration of the study
* If participant had prior allogeneic stem cell transplant (SCT), participant has evidence of ongoing graft-versus-host disease (GvHD)