Lenalidomide in Treating Patients With Multiple Myeloma Undergoing Autologous Stem Cell Transplant

Inclusion Criteria: * Patients must have active multiple myeloma requiring treatment (Durie-Salmon stage \>= 1) and have stable disease or be responsive to at least 2 months of any induction therapy; patients with smoldering myeloma are not eligible unless the disease has progressed to \>= stage 1 * No more than 12 months of any prior therapy, including CC-5013 and thalidomide * Within 12 months of initiation of induction therapy * No prior progression after initial therapy; in addition, no more than two regimens will be allowed excluding dexamethasone alone * No prior peripheral blood, bone marrow, or solid organ transplant * Patients must have peripheral blood stem cell collection of \>= 2 x 10\^6 cluster of differentiation (CD)34+ cells/kg (patient body weight) and preferably 5 x 10\^6 cells/kg (patient body weight); stem cells may be collected at any time prior to transplant; peripheral blood stem cell collection may occur before or after registration * Patients must have Eastern Cooperative Oncology Group (ECOG) performance status of 0-1 * Patients must have diffusing capacity of the lung for carbon monoxide (DLCO) \> 50% predicted with no symptomatic pulmonary disease * Patients must have left ventricular ejection fraction (LVEF) \>= 40% by multi gated acquisition scan (MUGA) or echocardiogram * Patients must not have uncontrolled diabetes mellitus * Patients must not have an active serious infection * Patients must not be human immunodeficiency virus (HIV), hepatitis …