Study of Bortezomib and Revlimid™ for Patients Relapsing or Progressing on Total Therapy II

Inclusion Criteria:

* History of histologically documented Multiple Myeloma (MM) previously enrolled on UARK 98-026 with relapsed or progressive disease after at least one autologous transplant.
* Patient has measurable disease in which to capture response, defined as: a. Serum M-protein level \> or =1.0 gm/dl (10.0 g/L) measured by serum protein electrophoresis or immunoglobulin electrophoresis b. Urinary M-protein excretion \> or =200 mg/24 hrs c. Bone marrow plasmacytosis of \> or =30% by bone marrow aspirate and/or biopsy d. Serum Free Light Chains (By the Freelite test) \> 2X normal.
* Performance status of \< or = 2 as per Zubrod scale, unless PS of 3 based solely on bone pain.
* Patients must have a platelet count \> or = 50,000/mm3, and an ANC of at least 1,000/μl.
* Patients must have adequate renal function defined as serum creatinine \< or =3.0 mg/dl.
* Patients must have adequate hepatic function defined as serum transaminases and direct bilirubin \< or =2 x the upper limit of normal.
* Pregnant or nursing women may not participate. Women of childbearing potential must have a negative pregnancy documented within one week of registration. Women of reproductive potential may not participate unless they have agreed to use an effective contraceptive method.
* Male or female adults of at least 18 years of age.
* Patients must have signed an IRB-approved written informed consent form and demonstrate willingness to meet follow-up schedule and study procedure obligations

Exclusion Criteria:

* Chemotherapy or radiotherapy received within the previous 2 weeks.
* Not previously enrolled on UARK 98-026.
* Has received either CC-5013 or bortezomib therapy after discontinuing from UARK 98-026.
* Significant neurotoxicity, defined as grade \> or = 2 neurotoxicity per NCI Common Toxicity Criteria.
* Platelet count \< 50,000/mm3, or ANC \< 1,000/μl
* POEMS Syndrome
* Clinically significant hepatic dysfunction as noted by bilirubin or AST \>3 times the upper normal limit or clinically significant concurrent hepatitis.
* New York Hospital Association (NYHA) Class III or Class IV heart failure
* Myocardial infarction within the last 6 months.
* Non-secretory MM, unless the patient has measurable lesions on CT, MRI and/or PET.
* Uncontrolled, active infection requiring IV antibiotics.
* Patients with a history of treatment for clinically significant ventricular cardiac arrhythmias.
* Poorly controlled hypertension, diabetes mellitus, or other serious or psychiatric illness that could potentially interfere with the completion of treatment according to this protocol.
* Pregnant or potential for pregnancy. Women of childbearing potential will have a pregnancy test at screening, and will be required to use a medically approved contraceptive method. Pregnancy testing will be performed prior to administration of each cycle of study drug.
* Breast-feeding women may not participate.
* Known hypersensitivity to thalidomide.