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