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

This phase II trial studies how well abatacept, ixazomib citrate, and dexamethasone work in treating patients with multiple myeloma that is resistant to chemotherapy. Abatacept may block certain proteins that are present on multiple myeloma cells that have been shown to protect against chemotherapy. Drugs used in chemotherapy, such as ixazomib citrate and dexamethasone, work in different ways to stop the growth of tumor cells, either by killing the cells, by stopping them from dividing, or by stopping them from spreading. Giving abatacept, ixazomib citrate, and dexamethasone may work better at treating patients with multiple myeloma resistant to chemotherapy.

PRIMARY OBJECTIVES:

I. To determine the therapeutic efficacy (as measured by response rate) of abatacept + ixazomib citrate (ixazomib) + dexamethasone in multiple myeloma patients who have relapsed (or who are primary refractory) following treatment with their first proteasome inhibitor-containing regimen (excluding ixazomib), compared to historical controls of ixazomib + dexamethasone.

SECONDARY OBJECTIVES:

I. To assess the toxicity profile of abatacept + ixazomib + dexamethasone in multiple myeloma patients who have relapsed (or who are primary refractory) following treatment with their first proteasome inhibitor-containing regimen, compared to historical controls of ixazomib + dexamethasone.

II. To assess progression-free and overall survival profile of abatacept + ixazomib + dexamethasone in multiple myeloma patients who have relapsed (or who are primary refractory) following treatment with their proteasome inhibitor-containing regimen, compared to historical controls of ixazomib + dexamethasone.

TERTIARY OBJECTIVES:

I. Assess whether myeloma expression of CD28, CD86, serum kynurenine and/or IL-6 are correlated with specific clinical outcomes.

OUTLINE:

Patients receive abatacept intravenously (IV) over 30 minutes on day 1 of course 1, then subcutaneously (SC) on days 2, 8, 15, and 22 of course 1, and then on days 1, 8, 15, and 22 of subsequent courses. Patients also receive ixazomib citrate orally (PO) once daily (QD) on days 1, 8, and 15 and dexamethasone on days 1, 8, 15, and 22. Courses repeat every 28 days in the absence of disease progression or unacceptable toxicity.

After completion of study treatment, patients are followed up at 30 days and then every 3 months thereafter.

Eligibility Criteria:
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

Exclusion Criteria:

* Prior treatment with ixazomib
* Inability to take ixazomib or abatacept
* Life expectancy less than 4 months
* Patients with a known diagnosis of plasma cell leukemia
* Known active tuberculosis or fungal infection
* Known seropositive for or active viral infection with, human immunodeficiency virus (HIV), hepatitis B virus (HBV) or hepatitis C virus (HCV)
* Uncontrolled intercurrent illness including, but not limited to, ongoing or active infection, symptomatic congestive heart failure, unstable angina pectoris, cardiac arrhythmia, or psychiatric illness/social situations that would limit compliance with study requirements
* Any condition, including the presence of laboratory abnormalities, which places the subject at unacceptable risk if he/she were to participate in the study or, which confounds the ability to interpret data from the study
* Pregnant or nursing female participants
* Unwilling or unable to follow protocol requirements
* Any condition which in the investigator?s opinion deems the participant an unsuitable candidate to receive study drug
* Received an investigational agent within 30 days prior to enrollment