Alternating Ixazomib Citrate and Lenalidomide as Maintenance Therapy After Stem Cell Transplant in Treating Patients With Multiple Myeloma

Inclusion Criteria: * Eastern Cooperative Oncology Group (ECOG) performance status and/or other performance status 0, 1, or 2 * Any autologous patient who underwent high dose melphalan (\>= 140 mg/m\^2) therapy/peripheral blood stem cell (PBSC) rescue for any stage of multiple myeloma and did not participate in another clinical transplant trial whose primary endpoint is also evaluating long-term, disease-free survival or survival; consenting for study between 30 days to 120 days after transplant; earliest can start therapy is 30 days post transplant after recovered from acute toxicity of autologous stem cell transplant (ASCT) * Voluntary written consent must be given before performance of any study related procedure not part of standard medical care, with the understanding that consent may be withdrawn by the patient at any time without prejudice to future medical care * Female patients who: * Are postmenopausal for at least 1 year before the screening visit, OR * Are surgically sterile, OR * If they are of childbearing potential, agree to practice 2 effective methods of contraception, at the same time, from the time of signing the informed consent form through 90 days after the last dose of study drug, OR * Agree to practice true abstinence when this is in line with the preferred and usual lifestyle of the subject; (periodic abstinence \[e.g., calendar, ovulation, symptothermal, post-ovulation methods\] and withdrawal are not acceptable methods of contraception) * …