Ixazomib Citrate and Lenalidomide After Stem Cell Transplant in Treating Patients With Newly Diagnosed Multiple Myeloma

Inclusion Criteria: * Patient must have undergone autologous stem cell transplantation, with melphalan as a preparative regimen, within 12 months of initiation of induction therapy for newly diagnosed myeloma * Time to initiation of maintenance therapy; patients may start maintenance therapy as early as 60 days post-transplant and up to 180 days post-transplant; as long as they meet the following criteria: * Platelet count \>= 100,000/mm\^3; platelet transfusions to help patients meet eligibility criteria are not allowed within 3 days before study enrollment * Neutrophil count \>= 1000/mm\^3; (no growth factors within 5 days prior to first dose of the study drug) * Total bilirubin =\< 1.5 x upper limit of normal (ULN) * Alanine aminotransferase (ALT) and aspartate aminotransferase (AST) =\< 3 x ULN * Creatinine \< 2.5 mg/dL * Recovered (i.e., =\< grade 1 toxicity) from the reversible effects of autologous stem cell transplant * Patients whose primary therapy was changed due to suboptimal response of toxicity will be eligible, however no more than 2 regimens will be allowed prior to ASCT * Patients must have an Eastern Cooperative Oncology Group (ECOG) status of 0 to 2 * Voluntary written informed consent before performance of any study-related procedure not part of normal medical care, with the understanding that consent may be withdrawn by the subject at any time without prejudice to future medical care * Female patients who: are postmenopausal for at least 1 year before th…