Phase II Study of IRD (Ixazomib, Lenalidomide, Dexamethasone) Post Autologous Stem Cell Transplantation Followed by Maintenance Ixazomib or Lenalidomide for Multiple Myeloma

Inclusion Criteria

Each patient must meet all of the following inclusion criteria to begin IRD Consolidation:

* Between the ages of 18 and 70 years of age (inclusive) at time of enrollment
* 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of any study-related procedure not part of standard medical care, with the understanding that consent may be withdrawn by the patient at any time without prejudice to future medical care
* Confirmed diagnosis of symptomatic multiple myeloma. (Patients with multiple myeloma with secondary amyloidosis are eligible.)
* Received at least two cycles of any regimen as initial systemic therapy for multiple myeloma and are within 2-16 months of the first dose of initial therapy
* Eastern Cooperative Oncology Group (ECOG) performance status and/or other performance status 0, 1, or 2
* Adequate organ function as defined below:

Absolute neutrophil count (ANC) \>= 1,000 mm\^3 Platelet count \>= 75,000/mm\^3; platelet transfusions to help patient meet eligibility criteria are not allowed within 7 days before study enrollment Total bilirubin \<= 1.5 x upper limit of normal range (ULN) Alanine aminotransferase (ALT) and aspartate aminotransferase (AST) \<=3 x ULN Calculated creatinine clearance \>= 30 mL/min

* Women of childbearing potential must follow pregnancy testing requirements as outlined in the Revlimid REMS program material. This is defined as either committing to continued abstinence from heterosexual intercourse or beginning TWO acceptable methods of contraception (one highly effective method and one additional effective method AT THE SAME TIME) at least 28 days prior to the start of lenalidomide, for the duration of study participation, and for 28 days following the last dose of lenalidomide. Women of childbearing potential must also agree to ongoing pregnancy testing.
* Men must agree to use a latex condom during sexual contact with a woman of childbearing potential even if they have had a successful vasectomy. All patients must be counseled at a minimum of every 28 days about pregnancy precautions and risks of fetal exposure. Should a woman become pregnant or suspect she is pregnant while participating in this study, she must inform her treating physician immediately.
* All study participants must be registered into the mandatory Revlimind REMS program and be willing to comply with its requirements. Per standard Revlimid REMS program requirements, all physicians who prescribe lenalidomide for research subjects enrolled into this trial, must be registered in, and must comply with, all requirements of the Revlimid REMS program.

Exclusion Criteria

Patients meeting any of the following exclusion criteria are not to be enrolled in the study:

* Female patients who are lactating or have a positive serum pregnancy test during the screening period
* Evidence of MM disease progression any time prior to enrollment. Progression from smoldering/asymptomatic MM to symptomatic MM is not exclusionary.
* Tandem autologous transplantation
* History of plasma cell leukemia or MM CNS involvement
* Administration or planned administration of any other concomitant chemotherapy, immunotherapy, radiotherapy, or any ancillary therapy which would be considered a treatment of multiple myeloma until Day +28 post-transplant through discontinuation from study. Patients may be on corticosteroids if they are being given for disorders other than multiple myeloma (e.g., adrenal insufficiency, rheumatoid arthritis, etc.)
* Any serious medical or psychiatric illness that could, in the investigator's opinion, potentially interfere with the completion of treatment according to this protocol.
* Prior organ transplant requiring immunosuppressive therapy
* Active hepatitis A, B or C virus infection, or known human immunodeficiency virus (HIV) positive
* Known allergy to any of the study medications, their analogues, or excipients in the various formulations of any agent
* Known GI disease or GI procedure that could interfere with the oral absorption or tolerance of ixazomib
* Concurrent hematologic or non-hematologic malignancy requiring treatment (other than multiple myeloma and secondary amyloidosis)
* Cardiac syncope, uncompensated NYHA Class 3 or 4 congestive heart failure, myocardial infarction within the previous six months, unstable angina pectoris, clinically significant repetitive ventricular arrhythmias despite antiarrhythmic treatment, severe orthostatic hypotension, or clinically important autonomic disease
* Grade \>= 3 peripheral neuropathy, or Grade 2 with pain on clinical examination during the screening period
* Major surgery within 14 days prior to enrollment
* Infection requiring systemic antibiotic therapy or other serious infection within 14 days prior to enrollment
* Participation in other clinical trials, including those with other investigational agents not included in this trial, within 30 days prior to enrollment and throughout the duration of this trial