Testing the Addition of Ixazomib/Placebo to Lenalidomide in Patients With Evidence of Residual Multiple Myeloma, OPTIMUM Trial

Inclusion Criteria:

* STEP 0: PRE-REGISTRATION
* Patient must be \>= 18 years of age
* Patient must be previously diagnosed with multiple myeloma (MM) and be on lenalidomide maintenance with \>= 5mg daily for at least 6 months and no more than 18 months after an early autologous stem cell transplantation (SCT =\< 12 months of diagnosis). Patient must not be off lenalidomide maintenance therapy for more than 30 days prior to start of treatment on Step 1 of this protocol
* Patient must be able to undergo a diagnostic bone marrow aspirate following pre-registration to Step 0

  * NOTE: A bone marrow aspirate specimen must be submitted to Mayo Clinic Hematology Laboratory for central assessment of minimal residual disease (MRD) status to confirm patient's eligibility for Step 1 randomization. Mayo Clinic will forward results to the submitting institution within three (3) business days of receipt of the bone marrow specimen
* Patient must have an Eastern Cooperative Oncology Group (ECOG) performance status 0, 1, or 2
* Patient must have been able to maintain at least 5mg daily dose of lenalidomide without growth factor support
* Human immunodeficiency virus (HIV)-infected patients on effective anti-retroviral therapy with undetectable viral load within 6 months are eligible for this trial
* STEP 1 RANDOMIZATION
* Patient must meet Step 0 eligibility criteria at the time of Step 1 randomization
* Patients must have evidence of residual disease by central MRD testing or by presence of monoclonal protein in serum or urine
* Patient must have serum protein electrophoresis (SPEP), urine protein electrophoresis (UPEP), and serum free light chain (FLC) performed =\< 28 days prior to randomization

  * NOTE: UPEP (on a 24-hour collection) is required, no substitute method is acceptable. Urine must be followed monthly if the baseline urine M-spike is \>= 200 mg/24 hour (hr). Please note that if both serum and urine M-components are present, both must be followed in order to evaluate response
* Hemoglobin \>= 8 g/dL (obtained =\< 14 days prior to randomization)
* Untransfused platelet count \>= 75,000 cells/mm\^3 (obtained =\< 14 days prior to randomization)
* Absolute neutrophil count (ANC) \>= 1000 cells/mm\^3 (obtained =\< 14 days prior to randomization)
* Calculated creatinine clearance \>= 30 mL/min (obtained =\< 14 days prior to randomization)
* Total bilirubin =\< 1.5 times the upper limit of normal (ULN) (obtained =\< 14 days prior to randomization)
* Serum glutamate pyruvate transaminase (SGPT) (alanine aminotransferase \[ALT\]) and serum glutamic oxaloacetic transaminase (SGOT) (aspartate aminotransferase \[AST\]) =\< 3 times the upper limit of normal (ULN) (obtained =\< 14 days prior to randomization)
* Patient must agree to register into the mandatory Revlimid Risk Evaluation and Mitigation Strategies (REMS) registered trademark program and be willing and able to comply with the requirements of Revlimid REMS registered trademark
* Patients of childbearing potential must either abstain from sexual intercourse for the duration of their participation in the study or agree to use TWO acceptable methods of birth control, one highly effective method and one additional effective method AT THE SAME TIME for 1) at least 28 days before starting study treatment; 2) while participating in the study; 3) during dose interruptions; and 4) for at least 90 days after the last dose of protocol treatment. Patients must also agree to not breastfeed during this same time period. Men must agree to either abstain from sexual intercourse for the duration of their participation in the study or use a latex condom during sexual contact with a partner of childbearing potential while participating in the study and for 90 days after the last dose of protocol treatment even if they have had a successful vasectomy. Patients must also agree to abstain from donating sperm while on study treatment and for 28 days after the last dose of protocol treatment even if they have had a successful vasectomy. All patients must agree to abstain from donating blood during study participation and for at least 28 days after the last dose of protocol treatment

Exclusion Criteria:

* Patient must not have primary refractory or progressive disease on a proteasome inhibitor-based regimen during induction therapy prior to stem cell transplant
* Patient must not be on other concurrent chemotherapy, or any ancillary therapy considered investigational

  * NOTE: Bisphosphonates are considered to be supportive care rather than therapy and are allowed while on protocol treatment
* Patient must not have uncontrolled psychiatric illness or social situations that would limit compliance with study requirements
* Patient must not have another malignancy requiring treatment or have received treatment within two years before pre-registration or previously diagnosed with another malignancy and have any evidence of residual disease. Patients with non-melanoma skin cancer or carcinoma in situ of any type are not excluded if they have undergone complete resection
* Patients must not have known gastrointestinal (GI) disease or GI procedure that could interfere with the oral absorption or tolerance of ixazomib or lenalidomide including difficulty swallowing
* Patient must not have known hepatitis B surface antigen-positive status or known or suspected active hepatitis C infection, but testing specifically for the trial is not required
* Patient must not be off lenalidomide maintenance therapy for more than 30 days prior to start of treatment on Step 1 of this protocol
* Patients must not have grade 2 or higher peripheral neuropathy or grade 1 peripheral neuropathy with pain per Common Terminology Criteria for Adverse Events (CTCAE)
* Patients must not have uncontrolled intercurrent illness
* Patients must not have grade 2 or higher diarrhea per CTCAE in the absence of antidiarrheals
* Patients must not have been on systemic treatment, within 14 days before the first dose of ixazomib, with strong CYP3A inducers (such as rifampin, rifapentine, rifabutin, carbamazepine, phenytoin, phenobarbital), or use of St. John's wort
* Patient must not be pregnant due to potential harm to the fetus from ixazomib and lenalidomide. All patients of childbearing potential must have a blood test or urine study with a sensitivity of at least 25 mIU/mL within 10-14 days prior to the first dose of lenalidomide and again within 24 hours prior to the first dose of lenalidomide. Patients of childbearing potential must also agree to ongoing pregnancy testing while on treatment. A patient of childbearing potential is defined as anyone, regardless of sexual orientation or whether they have undergone tubal ligation, who meets the following criteria: 1) has achieved menarche at some point, 2) has not undergone a hysterectomy or bilateral oophorectomy, or 3) has not been naturally postmenopausal (amenorrhea following cancer therapy does not rule out childbearing potential) for at least 24 consecutive months (i.e., has had menses at any time in the preceding 24 consecutive months)