Abatacept, Ixazomib Citrate, and Dexamethasone in Treating Patients With Multiple Myeloma Resistant to Chemotherapy

Inclusion Criteria

• •Patients with multiple myeloma who have relapsed (or who are primary refractory) following treatment with a proteasome inhibitor-containing regimen (excluding ixazomib) and who have not been treated with a second proteasome inhibitor (ixazomib, bortezomib, carfilzomib or other proteasome inhibitor).
• •Have an Eastern Cooperative Oncology Group (ECOG) performance status of =\< 2 at study entry
• •Must be free of systemic infection:
• •* Subjects with active infections (whether or not they require antibiotic therapy) may be eligible after complete resolution of the infection
• •* Subjects on antibiotic therapy must be off antibiotics for at least 7 days before beginning treatment
• •Absolute neutrophil count \>= 750/mm\^3
• •Platelet count \>= 25,000/mm\^3
• •Creatinine clearance \>= 30 mL/min
• •Total bilirubin =\< 3 x upper limit of normal (ULN)
• •Aspartate aminotransferase (AST) (serum glutamic-oxaloacetic transaminase \[SGOT\]) and alanine aminotransferase (ALT) (serum glutamate pyruvate transaminase \[SGPT\]) =\< 3 x ULN
• •Patient's multiple myeloma cells are positive for CD28 or CD86 expression by flow cytometry or immunohistochemistry (in any proportion) CD28 or CD86 positivity can have been determined on previous bone marrow aspirates or biopsies
• •Disease free of prior malignancies for \> 2 years with exception of currently treated basal cell, squamous cell carcinoma of the skin, or carcinoma ?in situ? of the cervix or breast
• •Participants of child-bearing potential must agree to use adequate contraceptive methods (e.g., hormonal or barrier method of birth control; abstinence) prior to study entry; should a woman become pregnant or suspect she is pregnant while she or her partner is participating in this study, she should inform her treating physician immediately
• •Participant must understand the investigational nature of this study and sign an Independent Ethics Committee/Institutional Review Board approved written informed consent form prior to receiving any study related procedure