S1211 Bortezomib, Dexamethasone, and Lenalidomide With or Without Elotuzumab in Treating Patients With Newly Diagnosed High-Risk Multiple Myeloma

Inclusion Criteria: * Patients must have newly diagnosed active multiple myeloma (MM) * For the Phase II portion only, patients must have high-risk MM based on one or more of the following criteria at the time of initial diagnosis (prior to any chemotherapy): * Poor-risk genomic signature according to the University of Arkansas 70-gene model (available clinically as myeloma prognostic risk score \[MyPRS\] score, Signal Genetics, Inc) AND/OR * Translocation (14;16), and/or translocation (14;20), and/or deletion (17p) by fluorescence in-situ hybridization (FISH) or cytogenetics AND/OR * Primary plasma cell leukemia (defined by either \>= 2,000 plasma cells/mL of peripheral blood, or 20% on a manual differential count) AND/OR * Serum lactate dehydrogenase (LDH) \>= 2 x institutional upper limit of normal (IULN) AND/OR * 1q21 amplification by FISH analysis AND/OR * High risk by the SKY92 signature * Patients with non-secretory MM or known amyloidosis are not eligible * Patients must have measurable disease within 28 days prior to registration (or prior to initiation of first induction course for patients with prior therapy) * Patients on the Phase I portion may not have received ANY prior chemotherapy; patients on the Phase II portion may have received one prior cycle of any non-investigational chemotherapy; prior chemotherapy must have been completed within 56 days prior to registration and all toxicities must have resolved to =\< grade 1; patients on either portio…