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 B surface antigen (HBSag), or hepatitis (Hep) C positive
* Patients must be non-pregnant and non-nursing; women of childbearing potential must have a negative serum or urine pregnancy test with a sensitivity of at least 25 mIU/mL 10-14 days prior to registration and repeated within 24 hours prior to the first dose of lenalidomide; in addition, women of childbearing potential taking lenalidomide must have a pregnancy test performed by the doctor weekly during the first 4 weeks of treatment, and then every 4 weeks if menses are regular and every 2 weeks if menses are irregular, and then 30 days following the last dose of lenalidomide; women of childbearing potential must either commit to continued abstinence from heterosexual intercourse or begin two acceptable methods of birth control - one highly effective method (intrauterine device \[IUD\], hormonal, tubal ligation, or partner's vasectomy), and one additional effective method (latex condom, diaphragm, or cervical cap) - at the same time, at least 4 weeks before she begins lenalidomide therapy; "women of childbearing" potential is defined as a sexually mature woman who has not undergone a hysterectomy or who has had menses at any time in the preceding 24 consecutive months; men must agree not to father a child and must use a latex condom during any sexual contact with women of childbearing potential while taking lenalidomide and for 4 weeks after therapy is stopped, even if they have undergone a successful vasectomy
* Absolute neutrophil count (ANC) \>= 1000/uL
* Platelets \>= 100,000/uL
* Creatinine clearance\* \>= 40 cc/min

  * To be calculated by method of Cockcroft-Gault or after 24-hour urine collection
* Creatinine =\< 2 mg/dL
* Total bilirubin =\< 2 mg/dL
* Aspartate aminotransferase (AST) =\< 3 x upper limits of normal
* Alkaline phosphatase =\< 3 x upper limits of normal
* Urine (U)-human chorionic gonadotropin (HCG) or serum HCG negative (if patient of childbearing potential)