Obatoclax and Bortezomib in Treating Patients With Relapsed or Refractory Multiple Myeloma

Inclusion Criteria: * Symptomatic multiple myeloma, meeting the following criteria at original diagnosis: * Bone marrow plasmacytosis with ≥ 10% plasma cells or sheets of plasma cells or biopsy proven plasmacytoma * Symptomatic disease (e.g.,anemia, hypercalcemia, bone disease, or renal dysfunction) that requires the initiation of therapy * Measurable diseases assessed by one of the following: * Monoclonal plasma cells detectable in the bone marrow * Monoclonal serum spike detectable by serum protein electrophoresis or immunofixation * Monoclonal protein detectable in the urine by electrophoresis or immunofixation * Abnormal levels of the serum free light chains with an abnormal ratio between kappa and lambda * Progressive disease after ≥ 1 prior therapy for myeloma * Previously treated with ≤ 10 courses (30 weeks) of bortezomib and had no disease progression during therapy OR completed bortezomib therapy within the past 6 weeks * No prior discontinuation of bortezomib therapy due to drug intolerance * No known brain metastases * No intracranial edema, intracranial metastasis, or active epidural disease * Patients with lytic lesions of the cranium secondary to myeloma are eligible * ECOG performance status 0-2 * Life expectancy \> 6 months * ANC ≥ 1,000/mm³ * Platelet count ≥ 50,000/mm³ * Bilirubin normal * AST and ALT ≤ 2.5 times upper limit of normal (ULN) * Creatinine ≤ 2 times ULN * Not pregnant or nursing * Negative pregnancy test * Fertile patients must use effective contraception * No peripheral neuropathy \> NCI toxicity grade 2 * No history of allergic reactions attributed to compounds of similar chemical or biologic composition to obatoclax mesylate or bortezomib * No concurrent uncontrolled illness including, but not limited to the following: * Ongoing or active infection * Symptomatic congestive heart failure * Unstable angina pectoris * Cardiac arrhythmia, including QTc \> 450 msec * Psychiatric illness/social situations that would limit compliance with study requirements * No history of seizure disorder * No other neurological disorder or dysfunction that, in the opinion of the investigator, would confound the evaluation of neurologic and other adverse events associated with obatoclax mesylate * At least 14 days since prior chemotherapy and recovered * More than 28 days since prior experimental drugs and/or investigational agents * No concurrent CYP interactive medications * No concurrent combination antiretroviral therapy for HIV-positive patients * No other concurrent anticancer therapy * Growth factors and bisphosphonates are allowed as medically indicated * Prednisone (≤ 10 mg per day) allowed provided there has been no dose increase within the past 2 weeks * No other concurrent investigational agents