Stem Cell Transplantation in Individuals With Multiple Myeloma (BMT CTN 0102)

Inclusion Criteria: * Meeting the Durie and Salmon criteria for initial diagnosis of MM * Stage II or III MM at diagnosis or anytime thereafter * Symptomatic MM requiring treatment at diagnosis or anytime thereafter * Received at least three cycles of initial systemic therapy and are within 2-10 months of initiation of the initial therapy (this time frame excludes the time for mobilization therapy) * If receiving chemotherapy-based mobilization regimens, must be able to receive high-dose melphalan between 2 and 8 weeks after the initiation of mobilization therapy whether delivered at the transplant center or at a referring center * Adequate organ function as measured by: 1. Cardiac: Left ventricular ejection fraction at rest greater than 40% 2. Hepatic: Bilirubin less than 2 times the upper limit of normal and alanine transaminase (ALT) and aspartate transaminase (AST) less than 3 times the upper limit of normal 3. Renal: Creatinine clearance greater than 40 ml/min (measured or calculated/estimated) 4. Pulmonary: Carbon monoxide diffusion (DLCO), Volume forcibly exhaled in one second (FEV1), and Forced Vital Capacity (FVC) greater than 50% of predicted value (corrected for hemoglobin), or O2 saturation greater than 92% of room air * An adequate autologous graft defined as a cryopreserved PBSC graft containing at least 4.0 x 106 CD34+ cells/kg patient weight; if prior to enrollment it is known that a patient will be on the auto-allo arm (i.e., a consenting, eligible HLA-matched sibling donor is available), the required autograft must contain at least 2.0 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; for patients without an HLA-matched sibling donor, the autograft must be stored so that there are two products each containing at least 2 x 10\^6 CD34+ cells/kg patient weight Exclusion Criteria: * Never advanced beyond Stage I MM since diagnosis * 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) * Plasma cell leukemia * Karnofsky performance score less than 70%, unless approved by the Medical Monitor or one of the Protocol Chairs * Uncontrolled hypertension * Uncontrolled bacterial, viral, or fungal infections (currently taking medication and progression of clinical symptoms) * 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 Medical Monitor or one of the Protocol Chairs; cancer treated with curative intent more than 5 years previously will be allowed * Pregnant or breastfeeding * Seropositive for the human immunodeficiency virus (HIV) * Unwilling to use contraceptive techniques during and for 12 months following treatment * Prior allograft or prior autograft * Received mid-intensity melphalan (more than 50 mg IV) as part of prior therapy * Prior organ transplant requiring immunosuppressive therapy