The purpose if this study is to evaluate the side effects of the combination of bortezomib and Revlimid (CC-5013) in patients with relapsed and relapsed/refractory multiple myeloma.

• Within 21 days of starting treatment the following tests will be performed: physical exam (including vital signs), ECG, neurological examination, blood tests, urine tests, bone marrow aspiration, x-rays and MRI or CT scan.
• Patients will receive bortezomib intravenously on day 1,4,8 and 11 followed by 10 days of rest. CC-5013 will be given orally on days 1-14 followed by 7-dyas of rest. One cycle lasts 21 days. This study will evaluate different dose levels of bortezomib and CC-5013 to see which dose level seems to be the best for most people. There will be 8 dose levels.
• Patients will be assigned to a dose level depending upon when they begin the study and how other dose levels have been tolerated by patients that are already on the study. Three to six patients will be treated at each dose level and will be observed for one full cycle. Depending upon the side effects, the dose level will increase, stay the same or be decreased by one level for the next group. 10 additional patients will be treated at the dose that is thought the best.
• On day four of the treatment cycle blood tests, vital signs and a review of side effects will be performed.
• On day eight of the the treatment cycle blood tests, vital signs, review of side effects and an ECG will be performed prior to medication administration. A bortezomib level will be taken before bortezomib infusion, 15 minutes, 1/2 hour, 45 minutes, 1 hour, 2 hours, 4 hours, 6 hours, 8 hours and 12 hours after the dose. Additional blood levels will be collected 24, 48, and 72 hours after the dose. (These blood levels will done during the first cycle only).
• On day 11 and day 14 of the treatment cycle blood tests, vital signs and review of side effects will be performed.
• After 2 cycles of treatment, the doctor will assess how the patient's disease is responding to the treatment. Additional tests such as bone marrow biopsy, x-rays or scans may be performed. If the disease is stable or getting better, patients will continue to receive repeated cycles of treatment. If the disease is getting worse, dexamethasone may be added to the treatment cycle.
• If dexamethasone is added, the dosing will start on days 1,2,4,5,8,9 and 11 of the 21-day cycle. The disease will then be reassessed after 2 additional cycles. If the disease is getting worse, the patient will be removed from the study.
• Once 8 cycles of treatment have been performed, the disease will be fully assessed again by blood tests, bone marrow biopsy, x-rays or scans. Again, if it is determined that the disease is stable of getting better, additional treatment cycles can be performed. If the disease is getting worse, treatment will be stopped..
• A follow-up visit will be scheduled one month after the last dose of the study drug and will include: physical exam, vital signs, neurological examination, and review of symptoms.
• Patients will remain on this study as long as the side effects are not too severe and the disease has not progressed.

Inclusion Criteria:

• Diagnosis of multiple myeloma based on standard diagnosis criteria: plasmacytomas on tissue biopsy; bone marrow plasmacytosis; monoclonal immunoglobulin spike on serum electrophoresis; lytic bone lesions.
• Must have relapsed or relapsed/refractory disease
• 18 years of age or older
• All baseline studies must be performed within 21 days of enrollment.
• ECOG performance status of 0 to 2

Exclusion Criteria:

• Renal insufficiency (serum creatinine levels > 2mg/dL)
• Concomitant therapy medications that include corticosteroids
• Peripheral neuropathy of Grade 3 or greater or painful Grade 2
• Evidence of mucosal or internal bleeding and/or platelet refractory
• ANC < 1000 cells/mm3
• Hemoglobin < 8.0 g/dL
• AST (SGOT and ALT) > 2 x ULN
• Intolerance to bortezomib or CC-5013 in the past or significant allergy to either compound, boron or mannitol
• Known hypersensitivity to thalidomide or the development of erythema nodosum
• Active infection or serious co-morbid medical condition
• Pregnant or breast-feeding women
• Prior malignancy with the last three years except adequately treated basal cell or squamous cell skin cancer, in situ cervical cancer, in situ breast cancer, on in-situ prostate cancer