The overall study design is that of biologic assignment, based on the availability of an HLA-matched sibling, to one of two treatment strategies for MM patients. Patients without an HLA-matched sibling will undergo tandem autologous transplants. Patients with an HLA-matched sibling will undergo an autologous transplant followed by a non-myeloablative allogeneic transplant. In addition, the tandem autologous transplant recipients will be randomized to either observation or one year of maintenance therapy to begin following the second autologous transplant. The large number of MM patients without an HLA-matched sibling enables us to evaluate the role of maintenance therapy following tandem autologous transplants.