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

Inclusion Criteria: * Histologically and clinically confirmed multiple myeloma * Relapsed or refractory disease after prior chemotherapy or transplantation\* * Measurable disease, defined by quantitative immunoglobulin levels in serum and/or urine and bone marrow plasmacytosis * Non-secretory disease allowed provided MRI or positron emission tomography or CT scan can accurately measure at least one plasmacytoma lesion * No known CNS involvement * Life expectancy \> 3 months * ECOG performance status (PS) 0-2 OR Karnofsky PS 60-100% * Absolute neutrophil count ≥ 1,000/mm³ (unless myelosuppression is secondary to bone marrow plasmacytosis \[\> 80% involvement\]) * Platelet count ≥ 50,000/mm³ (unless myelosuppression is secondary to bone marrow plasmacytosis \[\> 80% involvement\]) * Bilirubin ≤ 2 times upper limit of normal (ULN) * AST and ALT ≤ 2 times ULN * Creatinine \< 2 mg/dL OR creatinine clearance \> 40 mL/min * Not pregnant or nursing * Negative pregnancy test * Fertile patients must use effective contraception * Able to swallow pills * Patients with a history of seizures are eligible provided seizures are under adequate control with non-enzyme inducing anticonvulsant medication * No history of allergic reactions attributed to study agents * No sensory or motor neuropathy ≥ grade II * No uncontrolled current illness including, but not limited to, the following: * Ongoing or active infection * Symptomatic congestive heart failure * Unstable angina pectoris * Cardiac arrhythmia * Psychiatric illness or social situation that would limit study compliance * No grade 3 QT prolongation (i.e., \> 500 msec) at baseline * See Disease Characteristics * Prior bortezomib allowed * At least 2 weeks since prior therapy for multiple myeloma * Concurrent growth factors (filgrastim \[G-CSF\] and epoetin alfa) to sustain peripheral blood counts (during the first course of therapy only) allowed * Concurrent steroid therapy (≤ 20 mg of prednisone) for patients requiring chronic use for disorders other than myeloma allowed * No concurrent combination antiretroviral therapy for HIV-positive patients * No other concurrent investigational or commercial agents or therapies for this malignancy