A Study of Doxil, Vincristine and Decadron (DVd) +/ CC-5013 in Relapsed Refractory Multiple Myeloma (MM)

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.