Bortezomib, Liposomal Doxorubicin Hydrochloride, Dexamethasone, and Cyclophosphamide in Treating Patients With Multiple Myeloma That Relapsed After Autologous Stem Cell Transplant

Inclusion Criteria:

* Diagnosis of multiple myeloma that was symptomatic at the time of initial diagnosis
* Must have met the following criteria at one point during the disease course:

  * Bone marrow plasmacytosis with ≥ 10% plasma cells or sheets of plasma cells or biopsy-proven plasmacytoma
  * Symptomatic disease at initial diagnosis that prompted the initiation of therapy as well as evidence of end-organ damage at the time of diagnosis, including at least 1 of the following:

    * Anemia
    * Hypercalcemia
    * Bone disease (lytic bone lesions or pathologic fracture)
    * Renal dysfunction
* Disease relapsed \< 12 months after autologous stem cell transplantation (SCT)
* Measurable disease, as defined by the presence of ≥ 1 of the following:

  * Serum M-spike ≥ 1 g/dL
  * Urine M-spike ≥ 200 mg/24 hours
  * Involved free light chain (FLC) ≥ 10 mg/dL (provided the serum FLC is abnormal)
  * Plasma cells ≥ 30%
* ECOG performance status 0-2
* Negative pregnancy test
* Fertile patients must use effective contraception
* At least 14 days since prior palliative and/or localized radiotherapy
* Left ventricular ejection fraction (LVEF) normal by Echocardiography (ECHO) or multiple-gated acquisition (MUGA) scan
* Hemoglobin \> 8 g/dL
* Platelet count ≥ 75,000/mm\^3 (without transfusion support)
* Absolute neutrophil count (ANC) ≥ 1,000/mm\^3 (without use of growth factors)
* Creatinine \< 2.5 mg/dL
* Direct bilirubin ≤ 1.5 mg/dL
* Alanine aminotransferase (ALT) and aspartate aminotransferase (AST) ≤ 2.5 times upper limit of normal
* All tests below must be performed within 14 days prior to registration:

  * Serum free light chain assay
  * Kappa free light chain
  * Lambda free light chain
* Prior malignancy allowed provided it was treated curatively and has not relapsed in 5 years

  * Patients with basal cell skin cancer, in situ cervical cancer, or prostate cancer not requiring therapy are eligible

Exclusion Criteria:

* Therapy for relapsed disease following SCT
* Known allergy to bortezomib or anthracyclines
* Prior allogeneic SCT
* Peripheral neuropathy ≥ grade 2 according to the Cancer Therapy Evaluation Program (CTEP) active version of the NCI Common Terminology Criteria for Adverse Events (CTCAE)
* Concurrent uncontrolled illness that would limit study compliance, including the following:

  * Uncontrolled hypertension
  * Symptomatic congestive heart failure
  * Unstable angina
  * Uncontrolled cardiac arrhythmia
  * Uncontrolled psychiatric illness or social situation
  * Active uncontrolled infection
* Prior doxorubicin hydrochloride exposure \> 240 mg/m\^2
* Active, uncontrolled seizure disorder
* Seizures within the past 6 months
* Pregnant or nursing