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