Doxorubicin Hydrochloride Liposome, Melphalan, and Bortezomib in Treating Patients With Relapsed or Refractory Stage I, Stage II, or Stage III Multiple Myeloma

DISEASE CHARACTERISTICS: * Diagnosis of multiple myeloma * Stage I, II, or III disease according to Durie-Salmon staging criteria * Progressive disease, defined as one of the following: * For secretory disease: * A 25% increase in serum M-protein or Bence Jones protein (an absolute increase of 0.5 g/dL serum M-protein or ≥ 200 mg/24 hours of urine light chain excretion) * For nonsecretory disease: * Bone marrow biopsy with \> 25% increase in plasma cells or an absolute increase of ≥ 10% over prior known level * Development of new or worsening existing lytic bone lesions or soft tissue plasmacytomas * Hypercalcemia (i.e., calcium \> 11.5 mg/dL) * Relapsed after complete response * Must have received ≥ 2 of the following therapeutic regimens for multiple myeloma: * Nonmyeloablative transplantation * No significant graft-versus-host disease * At least 30 days since prior immunosuppressive therapy (concurrent prednisone allowed provided dose is ≤ 10 mg daily) * Mobilization with chemotherapy followed by either single or tandem autologous stem cell transplantation (considered 1 prior regimen) * Mobilization with chemotherapy followed by autologous and subsequent nonmyeloablative allogeneic stem cell transplantation (considered 1 prior regimen) * Any combination of drugs given concurrently (considered 1 prior regimen) PATIENT CHARACTERISTICS: * ECOG performance status 0-2 * Life expectancy ≥ 3 months * Absolute neutrophil count \> 1,000/mm\^3 (no colony-stimulating factors) * Platelet count \> 50,000/mm\^3 (no transfusion support) * Bilirubin ≤ 2.0 mg/dL * AST ≤ 4 times upper limit of normal * Not pregnant or nursing * Negative pregnancy test * Fertile patients must use effective contraception during and for 4 weeks after completion of study treatment * No history of allergic reaction to compounds containing boron or mannitol * No active uncontrolled viral (including HIV), bacterial, or fungal infection * No motor or sensory neuropathy ≥ grade 2 * No myocardial infarction within the past 6 months * No New York Heart Association class III or IV heart failure * No uncontrolled angina * No severe uncontrolled arrhythmia * No acute ischemia by EKG * LVEF ≥ 35% by MUGA (MUGA required in patients whose lifetime cumulative doxorubicin hydrochloride dose \> 400 mg/m\^2) PRIOR CONCURRENT THERAPY: * See Disease Characteristics * No grade III or IV toxicity due to previous antineoplastic therapy (except alopecia) * At least 3 weeks since prior chemotherapy * No prior doxorubicin HCl liposome, melphalan, and bortezomib as combination therapy (single or two-drug combinations of these are allowed) * No concurrent corticosteroids (≤ 10 mg prednisone/day or equivalent allowed) * No other concurrent chemotherapy * No concurrent thalidomide * No other concurrent investigational therapy * No other concurrent antineoplastic treatment for multiple myeloma, including clarithromycin * No concurrent radiation therapy * No concurrent nonsteroidal anti-inflammatory agents