Pomalidomide, Ixazomib Citrate, and Dexamethasone in Treating Patients With Previously Treated Multiple Myeloma or Plasma Cell Leukemia

Other malignancy requiring active therapy

* EXCEPTIONS: Non-melanoma skin cancer, ductal breast carcinoma in situ (DCIS) or carcinoma-in-situ of the cervix

* NOTE: If there is a history or prior malignancy, they must not be receiving other specific treatment for their cancer

Females of childbearing potential (FCBP)\* must have a negative serum pregnancy test with a sensitivity of at least 50 mIU/mL within 10-14 days prior to and again within 24 hours prior to prescribing pomalidomide for cycle 1 (prescriptions must be filled within 7 days as required by RevAssist \[lenalidomide REMS program\]), and must either commit to continued abstinence from heterosexual intercourse or begin TWO acceptable methods of birth control, one highly effective method and one additional effective method; AT THE SAME TIME, at least 28 days before she starts taking pomalidomide FCBP must also agree to ongoing pregnancy testing; men must agree to use a latex condom during sexual contact with a FCBP even if they have had a successful vasectomy; patient must follow pregnancy testing requirements as outlined in the POMALYST REMS program

* A female of childbearing potential is a sexually mature woman who: 1) has not undergone a hysterectomy or bilateral oophorectomy; or 2) has not been naturally postmenopausal for at least 24 consecutive months (i.e., has had menses at any time in the preceding 24 consecutive months)

Nursing women

Men or women of childbearing potential who are unwilling to employ adequate contraception

Other co-morbidity which would interfere with patient's ability to participate in trial, e.g. uncontrolled infection, uncompensated heart or lung disease

Other concurrent chemotherapy, radiotherapy, or any ancillary therapy considered investigational

* NOTE: Bisphosphonates are considered to be supportive care rather than therapy, and are thus allowed while on protocol treatment

Patient has \>= grade 3 peripheral neuropathy, or grade 2 with pain on clinical examination during the screening period

Major surgery =\< 14 days before study registration

Systemic treatment with strong CYP3A4 inducers (e.g. rifampin, rifapentine, rifabutin, carbamazepine, phenytoin, phenobarbital, gingko biloba, St. John's wort) within 7 days before registration

Evidence of current uncontrolled cardiovascular conditions, including cardiac arrhythmias, congestive heart failure, angina, or myocardial infarction within the past 6 months; Note: prior to study entry, any electrocardiogram (ECG) abnormality at screening must be documented by the investigator as not medically relevant

Corrected QT Interval (QTc) \> 470 milliseconds (msec) on a 12-lead ECG obtained during the screening period

* Note: If a machine reading is above this value, the ECG should be reviewed by a qualified reader and confirmed on a subsequent ECG

Known human immunodeficiency virus (HIV) positive

Known hepatitis B surface antigen-positive status, or known or suspected active hepatitis C infection

Any serious medical or psychiatric illness that could, in the investigator's opinion, potentially interfere with the completion of treatment according to this protocol

Known allergy to any of the study medications, their analogues or excipients in the various formulations

Known gastrointestinal (GI) disease or GI procedure that could interfere with the oral absorption or tolerance of ixazomib including difficulty swallowing

Diarrhea \> grade 1, based on the National Cancer Institute Common Terminology Criteria for Adverse Events (NCI CTCAE) grading, in the absence of antidiarrheals

What this study is about