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)

- No more than two lines of prior therapy for multiple myeloma, including the
autologous SCT (autologous SCT, preceding induction therapy, and any maintenance
therapy will be considered one line of therapy)

- No therapy for relapsed disease following 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

- Hemoglobin > 8 g/dL

- Platelet count ≥ 75,000/mm^3 (without transfusion support)

- ANC ≥ 1,000/mm^3 (without use of growth factors)

- Creatinine < 2.5 mg/dL

- Direct bilirubin ≤ 1.5 mg/dL

- ALT and AST ≤ 2.5 times upper limit of normal

- LVEF normal by ECHO or MUGA scan

- Not pregnant or nursing

- Negative pregnancy test

- Fertile patients must use effective contraception

- No active, uncontrolled seizure disorder

- No seizures within the past 6 months

- No 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

- No peripheral neuropathy ≥ grade 2 according to the CTEP active version of the NCI
CTCAE

- 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

- No known allergy to bortezomib or anthracyclines

- At least 14 days since prior palliative and/or localized radiotherapy

- No prior allogeneic SCT

- No prior doxorubicin hydrochloride exposure > 240 mg/m^2