Lenalidomide After Donor Stem Cell Transplant and Bortezomib in Treating Patients With High Risk Multiple Myeloma

Inclusion Criteria: * Symptomatic multiple myeloma by International Myeloma Working Group (IMWG) criteria according to the most recent updated version (International Myeloma Workshop \[IMW\] meeting in Paris 2011) * Must have received at least 3 of the following classes of anti-myeloma agents either alone or in combination: glucocorticoids, immunomodulatory drugs including thalidomide, proteasome inhibitors, alkylating chemotherapy, or anthracyclines * Must meet any of these criteria for high risk disease: * Relapse or progressive disease according to uniform response criteria within 2 years after starting first-line therapy or within 2 years after autologous stem cell transplant * Failure to achieve partial response (PR) within 6 months of staring first-line therapy * Presence of high risk cytogenetic features (t(14;16), t(14;20), deletion 17p) * Chromosome 14 translocations other than to chromosome 11 * Chromosome 1p deletion and 1q amplification * MyPRS gene expression score equal or higher than 45.2 * High risk 70 gene expression profile (MyPRS GEP70TM) * Any other high risk genetic profile that is determined by future IMWG consensus or by internal myeloma panel consensus; for the latter, any additional criteria will be submitted as an addendum * Diagnosis with multiple myeloma between the ages of 18-50 * Must have achieved at least a minor response to any previous regimen according to adapted European Group for Blood and Marrow Transplantation (EBMT) criteria * Must have suitable matched sibling or matched unrelated donor for stem cell source * Must be transplant-eligible per institution guidelines * Must have estimated glomerular filtration rate (eGFR) by Modification of Diet in Renal Disease (MDRD) formula or Cockroft-Gault formula of 50mL/min or higher * All study participants must be registered into the mandatory Revlimid REMS® program, and be willing and able to comply with the requirements of Revlimid REMS® * Females of childbearing potential must have negative serum or urine pregnancy test and use acceptable birth control methods * Able to take aspirin daily as prophylactic anticoagulation (patients intolerant to acetylsalicylic acid \[ASA\] may use warfarin or low molecular weight heparin) Exclusion Criteria: Participants must not: * Have known hypersensitivity to thalidomide or lenalidomide * Have progressive disease at the time of transplant * Uncontrolled concurrent significant medical or psychological co-morbidity * Grade 3 peripheral neuropathy * Known seropositive for or active viral infection with human immunodeficiency virus (HIV), hepatitis B virus (HBV) or hepatitis C virus (HCV); patients who are seropositive because of hepatitis B virus vaccine are eligible * Be females who are pregnant * Recent (within 3 years) history of other malignancies, excluding basal cell carcinoma or squamous cell carcinoma of the skin * Be currently enrolled in another investigational treatment protocol