Inclusion Criteria:

- Understand and voluntarily sign an informed consent form.

- Age greater than 18 years at the time of signing the informed consent form.

- Able to adhere to the study visit schedule and other protocol requirements.

- Diagnosed with active multiple myeloma and be considered to have disease progression
after at least 2 cycles of anti-myeloma treatment or have relapsed with progressive
disease after treatment.

- Measurable myeloma paraprotein levels in serum (≥ 0.5g/dL) or urine (≥ 0.2 g excreted
in a 24-hour collection sample).

- Eastern Cooperative Group (ECOG) Performance Status of 0-2. Performance status of 3
and 4 will be allowed if related to bony disease.

- Bilirubin < 2 x upper limits of normal (ULN).

- Liver enzymes (ALT or AST) < 3 x ULN.

- Must have adequate bone marrow function: * Absolute neutrophil count > 1,000
cells/mm3 (1.0 x 109/L) * Platelets ≥ 100,000 cells/mm3 (100 x 109/L) * Hemoglobin ≥
8 g/dL

- Must have adequate renal function: creatinine ≤ 2.5 mg/dL.

- Must have 2-d echocardiogram indicating LVEF ≥ 50% within 42 days prior to first dose
of study drug.

- Women of childbearing potential (WCBP) must have a negative serum or urine pregnancy
test within 7 days of starting study drug. In addition, sexually active WCBP must
agree to use adequate contraceptive methods (oral, injectable, or implantable
hormonal contraceptive; tubal ligation; intra-uterine device; barrier contraceptive
with spermicide; or vasectomized partner) while on study drug. WCBP must agree to
have pregnancy tests every 4 weeks while on study drug.

Exclusion Criteria:

- Severe infection requiring intravenous antibiotic treatment.

- Life expectancy of less than 3 months.

- Prior malignancy, except for adequately treated basal cell or squamous cell skin
cancer, in-situ cervical cancer, or other cancer from which the subject has been
disease-free for at least 5 years.

- Solitary bone or solitary extramedullary plasmacytoma as the only evidence of plasma
cell dyscrasia.

- Subjects who have received > 500mg/m2 of doxorubicin alone, or Doxil® alone, or
doxorubicin plus Doxil®.

- Prior treatment with CC-5013.

- Prior development of ≥ grade 2 (NCI CTC) allergic reaction/hypersensitivity while
taking thalidomide.

- Prior development of a ≥ grade 3 (NCI CTC) rash or any desquamation while taking
thalidomide.

- History of cardiac disease, with New York Heart Association Class II or greater.

- Uncontrolled medical problems such as diabetes mellitus, coronary artery disease,
hypertension, unstable angina, arrhythmias), pulmonary, hepatic and renal diseases
unless renal insufficiency is felt to be secondary to multiple myeloma.

- Any investigational agent or systemic anti-myeloma therapy within 28 days of the
first dose of treatment.

- Any serious medical condition, laboratory abnormality, or psychiatric illness that
would prevent the subject from signing the informed consent form.

- Pregnant or lactating females.

- Any condition, including the presence of laboratory abnormalities, which places the
subject at unacceptable risk if he/she were to participate in the study or confounds
the ability to interpret data from the study.