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

Inclusion Criteria: * Previously treated myeloma, currently with extramedullary disease (defined as plasmacytoma outside bone marrow that is not contiguous with a bone lesion) with at least one lesion that has a single diameter of \>= 2 cm or plasma cell leukemia (defined as circulating plasma cells exceeding 5% of peripheral blood leukocytes or 0.5 X 10\^9/L or 200 cells/150000 events by flow cytometry) * Calculated creatinine clearance (using Cockcroft-Gault equation) \>= 30 mL/min * Absolute neutrophil count (ANC) \>= 1000/mm\^3 * Platelet count \>= 50,000/mm\^3 * Hemoglobin \>= 8.0 g/dL * Patients with measurable disease defined as at least one of the following: * For patients with extramedullary disease (EMD) measurable disease by computed tomography (CT) or magnetic resonance imaging (MRI) or the CT portion of the positron emission tomography (PET)/CT: must have at least one lesion that has a single diameter of \>= 2 cm; skin lesions can be used if the area is \>= 2 cm in at least one diameter and measured with a ruler * Plasma cell count \>= 0.5 X 10\^9/L or 5 percent of the peripheral blood white cells * Plasma cell count if determined by flow cytometry, \>= 200/150,000 events * Eastern Cooperative Oncology Group (ECOG) performance status (PS) 0, 1 or 2 * Provide informed written consent * Negative pregnancy test done =\< 7 days prior to registration, for women of childbearing potential only * All study participants must be registered into the mandatory pomali…