Stem Cell Transplant With Lenalidomide Maintenance in Patients With Multiple Myeloma (BMT CTN 0702)

Inclusion Criteria: * Patients meeting the criteria for symptomatic multiple myeloma (MM). * Patients who are 70 years of age, or younger, at time of enrollment. * Patients who have received at least two cycles of any regimen as initial systemic therapy and are within 2 - 12 months of the first dose of initial therapy. * Cardiac function: left ventricular ejection fraction at rest greater than 40 percent. * Hepatic: bilirubin less than 1.5x the upper limit of normal and alanine aminotransferase (ALT) and aspartate aminotransferase (AST) less than 2.5x the upper limit of normal. (Patients who have been diagnosed with Gilbert's Disease are allowed to exceed the defined bilirubin value of 1.5x the upper limit of normal.) * Renal: Creatinine clearance of grater than or equal to 40 mL/min, estimated or calculated. * Pulmonary: Diffusing capacity of the lung for carbon monoxide (DLCO), forced expiratory volume in one second (FEV1), or forced vital capacity (FVC) greater than 50 percent of predicted value (corrected for hemoglobin). * Patients with an adequate autologous graft defined as a cryopreserved PBSC graft containing greater than or equal to 4 x 10\^6 CD34+ cells/kg patient weight. The graft may not be CD34+ selected or otherwise manipulated to remove tumor or other cells. The graft can be collected at the transplanting institution or by a referring center. The autograft must be stored so that there are two products each containing at least 2 x 10\^6 CD34+ cells/kg patient weight. * Signed informed consent form. Exclusion Criteria: * Patients who never fulfill the criteria for symptomatic MM. * Patients with purely non-secretory MM \[absence of a monoclonal protein (M protein) in serum as measured by electrophoresis and immunofixation and the absence of Bence Jones protein in the urine defined by use of conventional electrophoresis and immunofixation techniques\]. Patients with light chain MM detected in the serum by free light chain assay are eligible. * Patients with plasma cell leukemia. * Karnofsky performance score less than 70 percent. * Patients with greater than grade 2 sensory neuropathy (CTCAE). * Patients with uncontrolled bacterial, viral or fungal infections (currently taking medication and progression of clinical symptoms). * Patients seropositive for the human immunodeficiency virus (HIV). * Myocardial infarction within 6 months prior to enrollment or has New York Heart Association (NYHA) Class III or IV heart failure, uncontrolled angina, severe uncontrolled ventricular arrhythmias, or electrocardiographic evidence of acute ischemia or active conduction system abnormalities. Prior to study entry, any ECG abnormality at Screening has to be documented by the investigator as not medically relevant. * Patient has hypersensitivity to bortezomib, boron or mannitol. * Patient has received other investigational drugs with 14 days before enrollment. * Patients with prior malignancies except resected basal cell carcinoma or treated cervical carcinoma in situ. Cancer treated with curative intent less than 5 years previously will not be allowed unless approved by the Protocol Officer or one of the Protocol Chairs. Cancer treated with curative intent greater than 5 years previously is allowed. * Female patients who are pregnant (positive B-HCG) or breastfeeding. * Females of childbearing potential (FCBP) or men who have sexual contact with FCBP unwilling to use contraceptive techniques during the length of lenalidomide maintenance therapy. * Prior allograft or prior autograft. * Patients who have received mid-intensity melphalan (greater than 50 mg IV) as part of prior therapy. * Patients unable or unwilling to provide informed consent. * Prior organ transplant requiring immunosuppressive therapy. * Patients with disease progression prior to enrollment. * Patients who have received lenalidomide as initial therapy for MM and have experienced toxicities resulting in treatment discontinuation. * Patients who experienced thromboembolic events while on full anticoagulation during prior therapy with lenalidomide or thalidomide. * Patients unwilling to take deep vein thrombosis (DVT) prophylaxis. * Patients who cannot undergo an intervention in any treatment arm due to a priori denial of medical costs coverage by third party payers. * Patients unable to unwilling to return to the transplant center for their assigned treatments.