Vorinostat, Bortezomib, and Doxorubicin Hydrochloride Liposome in Treating Patients With Relapsed or Refractory Multiple Myeloma

DISEASE CHARACTERISTICS: * Diagnosis of multiple myeloma * Relapsed or refractory disease PATIENT CHARACTERISTICS: * ECOG performance status 0-2 * Life expectancy ≥ 3 months * ANC ≥ 1.0 x 10\^9/L (no granulocyte growth factor support, e.g., G-CSF or GM-CSF allowed) * Platelet count ≥ 100 x 10\^9/L (erythropoietin allowed, no platelet or RBC transfusion within the past 2 weeks) * Hemoglobin ≥ 8 g/dL (erythropoietin allowed, no platelet or RBC transfusion within the past 2 weeks) * Creatinine clearance ≥ 30 mL/min * AST or ALT ≤ 2.5 times upper limit of normal (ULN) * Total bilirubin ≤ 1.5 times ULN * Not pregnant or nursing * Negative pregnancy test * Fertile patients must use effective contraception during and for 3 months after completion of study treatment * LVEF ≥ 45% by MUGA or ECHO * Symptomatic neuropathy \< grade 2 * No known history of HIV * No active or serious infection, medical or psychiatric illness that would preclude study participation * No active hepatitis B or C infection * No other prior or concurrent malignancy except for adequately treated basal cell or squamous cell carcinoma of the skin, in situ malignancy, low-risk prostate cancer after curative therapy, or other cancer for which the patient has been disease-free for ≥ 3 years * No history of hypersensitivity reaction to bortezomib or any of its components (boron, mannitol), vorinostat, doxorubicin hydrochloride, or any of the components of PLD * No serum potassium ≤ 3.0 or serum magnesium ≤ 1.6 that cannot be corrected with supplementation are excluded * Patients must have adequate cardiovascular function, defined by all of the following: * No EKG evidence of active, clinically significant conduction system abnormalities * No EKG evidence of QTc prolongation \> grade 2 * NOTE: Any EKG abnormality at screening has to be documented by the investigator as not medically significant. PRIOR CONCURRENT THERAPY: * No limit to number of prior treatment regimens * At least 30 days since prior therapy and recovered * At least 3 months since prior autologous stem cell transplantation and recovered * Prior allogeneic stem cell or bone marrow transplantation allowed provided the following criteria are met: * More than 1 year since transplantation * No longer receiving immunosuppressive therapy or treatment for graft-versus-host disease (GVHD) prophylaxis * No active GVHD * No active, uncontrolled infections * No major surgery within the past 3 weeks * No prior anthracycline dose \> 360 mg/m\^2 for doxorubicin hydrochloride (including pegylated liposomal doxorubicin hydrochloride \[PLD\]) or 720 mg/m\^2 for epirubicin hydrochloride * No prior or concurrent histone deacetylase inhibitor (e.g., valproic acid) * No concurrent filgrastim (G-CSF) or sargramostim (GM-CSF) during course 1 * No other concurrent investigational or anticancer agent