Carfilzomib, Lenalidomide, and Dexamethasone Before and After Stem Cell Transplant in Treating Patients With Newly Diagnosed Multiple Myeloma

Inclusion Criteria: * Newly diagnosed, myeloma requiring systemic chemotherapy as per International Myeloma Working Group (IMWG) uniform criteria: * Prior treatment of hypercalcemia or spinal cord compression or active and/or aggressively progressing myeloma with corticosteroids or lenalidomide or bortezomib-based regimens does not disqualify the patient (the treatment dose should not exceed the equivalent of 160 mg of dexamethasone in a 4 week period or not more than 1 cycle) * Bisphosphonates are permitted * Suitable and interested to proceed to ASCT * Measurable disease, prior to initial treatment as indicated by one or more of the following: * Serum monoclonal (M)-protein \>= 0.5 g/dL * Urine M-protein \>= 200 mg/24 hours * If serum protein electrophoresis is felt to be unreliable for routine M-protein measurement, then quantitative immunoglobulin levels are acceptable * Life expectancy of more than 3 months * Eastern Cooperative Oncology Group (ECOG) performance status 0-2 * Bilirubin \< 1.5 times the upper limit of normal (ULN) * Aspartate aminotransferase (AST) and alanine aminotransferase (ALT) \< 2.5 times ULN * Absolute neutrophil count (ANC) \>= 1.0 x 10\^9/L * Hemoglobin \>= 8 g/dL * Platelet count \>= 75 x 10\^9/L; subjects may receive red blood cell (RBC) transfusions or platelet transfusions, if clinically indicated in accordance with institutional guidelines; however, screening platelet count should be independent of platelet transfusions for at l…