Pomalidomide in Gene Expression Profiling (GEP)-Defined High-risk Multiple Myeloma

Inclusion Criteria: * Participant has multiple myeloma, relapsed or resistant to prior therapy. * Participant has high-risk disease, as defined by any of the following: * GEP risk score of \> 0.66 OR * Metaphase based abnormalities of 1q or 1p OR * LDH \> 360 U/L * Participant has received prior therapy with lenalidomide-containing regimen and has been determined to be refractory, resistant, or relapsed. * Participant has no significant peripheral neuropathy (\< grade 3 by the most current NCI CTCAE version) * Participant has adequate hematopoietic reserve as defined by platelet count ≥ 50,000/µL and ANC of \> 1000/µL. * Participant has adequate renal function as defined by serum creatinine \< 2 mg/dL. * Participant has adequate hepatic function, defined by serum Total bilirubin \</= 1.5 mg/dL and AST (SGOT) and ALT (SGPT) \</= x ULN. * Participant is 18 years of age or greater. * Participant has not received anti-cancer therapy within 4 weeks prior to treatment on this study. * Zubrod ≤ 2, unless solely due to symptoms of MM-related bone disease. * Disease free of prior malignancies for \>/= 5 years with exception of currently treated basal cell, squamous cell carcinoma of the skin, or carcinoma in situ of the cervix or breast. * Females of childbearing potential (FCBP)† must have a negative serum or urine pregnancy test with a sensitivity of at least 25 mIU/mL within 10 - 14 days prior to and again within 24 hours prior to starting lenalidomide or CC-4047 and must either commit to continued abstinence from heterosexual intercourse or begin TWO acceptable methods of birth control, one highly effective method and one additional effective method AT THE SAME TIME, at least 28 days before she starts taking lenalidomide or CC-4047. * All patients must be informed of the investigational nature of this study and must sign and give written voluntary consent in accordance with institutional and federal guidelines. * Willing and able to take aspirin or alternate prophylactic anticoagulation. Exclusion Criteria: * Any serious medical condition, laboratory abnormality, or psychiatric illness that would prevent the subject from signing the informed consent form. * Pregnant or breast feeding females. * Men unwilling to use a condom (even if they have undergone a prior vasectomy) while having intercourse with any woman, while taking the drug and for 4 weeks after stopping treatment. * 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. * Use of any other experimental drug or therapy within 28 days of baseline. * Known hypersensitivity to lenalidomide. * The development of erythema nodosum if characterized by a desquamating rash while taking lenalidomide, CC-4047 or similar drugs. * Any prior use of CC-4047. * Concurrent use of other anti-cancer agents or treatments. * Known seropositive for or active viral infection with human immunodeficiency virus (HIV), hepatitis B virus (HBV) or hepatitis C virus (HCV). Patients who are seropositive because of hepatitis B virus vaccine are eligible. * Active malignancy (exception of non melanoma skin cancer or in situ cervical or breast cancer). * Active DVT or PE that has not been therapeutically anticoagulated. * ≥ grade 3 peripheral neuropathy.