Inclusion Criteria:

- Cohort 1: Relapsed, refractory patients with multiple myeloma who have failed at
least one prior regimen not including dexamethasone alone

- Cohort 2: Newly diagnosed patients with previously untreated multiple myeloma; prior
dexamethasone permitted; not to exceed 320 mg

- Diagnosis of multiple myeloma with quantifiable monoclonal protein or light chain
identified by serum protein electrophoresis (SPEP), urine protein electrophoresis
(UPEP), or serum free light chain assay

- Eastern Cooperative Oncology Group (ECOG) performance status 0-2

- Absolute neutrophil count >= 1.5

- Platelet count >= 75,000 unless slightly lower due to disease with the approval of
the principal investigator (PI)

- Serum creatinine =< 2.0 mg/dL

- Serum bilirubin =< 1.2

- Aspartate transaminase (AST)/alanine transaminase (ALT) =< 2.5 x upper limit of
normal (ULN)

- Alkaline phosphatase =< 2.5 x ULN

- Voluntary written informed consent before performance of any study-related procedure
not part of normal medical care, with the understanding that consent may be withdrawn
by the subject at any time without prejudice to future medical care

- Left ventricular ejection fraction greater than or equal to 50% by multi gated
acquisition scan (MUGA)

- Female subjects must be post-menopausal, surgically sterilized, or willing to use an
acceptable method of birth control (i.e., a hormonal contraceptive, intra-uterine
device, diaphragm with spermicide, condom with spermicide, or abstinence) for the
duration of the study; female patients of childbearing potential must have a negative
serum pregnancy test within 2 weeks prior to enrollment

- Male patients must use an effective contraceptive method during the study and for a
minimum of 6 months after study treatment

Exclusion Criteria:

- Current concomitant chemotherapy, radiation therapy, or immunotherapy other than as
specified in the protocol

- Use of other anticancer therapy within 15 days or before study entry; the patient
must have recovered from all acute non-hematological toxicities from any previous
therapy

- Have any other severe concurrent disease, or have a history of serious organ
dysfunction or disease involving the heart, kidney, liver, or other organ system that
may place the patient at undue risk to undergo treatment, despite appropriate
antibiotics or other treatment; for cardiac dysfunction, myocardial infarction within
6 months prior to enrollment or New York Heart Association (NYHA) Class III or IV
heart failure, uncontrolled angina, severe uncontrolled ventricular arrhythmias, or
electrocardiographic evidence of acute ischemia or active conduction system
abnormalities

- Patients with a systemic fungal, bacterial, viral, or other infection not controlled
(defined as exhibiting ongoing signs/symptoms related to the infection) on antiviral,
antibiotic and antifungal treatment

- Patient has >= Grade 2 peripheral neuropathy within 14 days before enrollment

- Patient has hypersensitivity to bortezomib, boron or mannitol

- Pregnant or lactating patients

- Cumulative dose of doxorubicin of 400 mg/m^2 or greater, or if this level would be
exceeded during the current study

- Any significant concurrent illness, condition, or psychiatric disorder that would
compromise patient safety or compliance, interfere with consent, study participation,
follow up, or interpretation of study results

- Have had a diagnosis of another malignancy, unless the patient has been disease-free
for at least 3 years following the completion of curative intent therapy including
the following:

- Patients with treated non-melanoma skin cancer, in situ carcinoma, or cervical
intraepithelial neoplasia, regardless of the disease-free duration, are eligible for
this study if definitive treatment for the condition has been completed;

- Patients with organ-confined prostate cancer with no evidence of recurrent or
progressive disease based on prostate-specific antigen (PSA) values are also eligible
for this study if hormonal therapy has been initiated or a radical prostatectomy has
been performed;

- Prior autologous stem cell transplant (Cohort 2 only);

- Prior allogeneic stem cell transplant;

- Patient has received other investigational drugs within 14 days before enrollment