CB-839 HCl in Combination With Carfilzomib and Dexamethasone in Treating Patients With Recurrent or Refractory Multiple Myeloma

Inclusion Criteria: * Patients must have relapsed and/or refractory myeloma and be experiencing disease relapse * Patients must have measurable disease by International Myeloma Working Group (IMWG) criteria (any of the following): * Serum M-protein \>= 0.5 g/dL or for IgA myeloma, an elevated IgA level by quantitative IgA nephelometry * Urine M-protein \>= 200 mg in a 24-hour collection * Serum free light chain level \>= 10 mg/dL with an abnormal free light chain ratio * Measurable plasmacytoma by cross sectional imaging (computed tomography \[CT\], magnetic resonance imaging \[MRI\] or \[18F\]-fluorodeoxyglucose positron emission tomography with CT \[FDG PET/CT\]) * 20% or more light chain restricted, clonal plasma cells in the bone marrow * At least two prior lines of therapy and all patients should have at least been exposed to a proteasome inhibitor (PI), an immunomodulatory drug (IMiD), and an anti-CD38 antibody * Eastern Cooperative Oncology Group (ECOG) performance status =\< 2 (Karnofsky \>= 60%) * Leukocytes \>= 3,000/mcL * Absolute neutrophil count \>= 1,000 cells/mm3 without growth factors (within 14 days of enrollment) * Hemoglobin \>= 8 g/dL (within 14 days of enrollment) * Platelets \>= 50,000 cells/mm3 (\>= 30,000 cells/mm3 if bone marrow plasma cells \>= 50% at enrollment) * Total bilirubin =\< 1.5 x upper limit of normal (ULN) * Aspartate aminotransferase (AST) (serum glutamic-oxaloacetic transaminase \[SGOT\])/alanine aminotransferase (ALT) (serum glutamate pyruvate transaminase \[SGPT\]) =\< 3 x institutional ULN * Creatinine =\< institutional ULN OR glomerular filtration rate (GFR) \>= 40 mL/min/1.73 m\^2 for patients with creatinine levels above institutional normal * Willingness to undergo interim bone marrow biopsy/aspiration for clinical purposes * Negative pregnancy test done =\< 7 days prior to registration, for women of childbearing potential only * The effects of CB-839 HCl on the developing human fetus are unknown. For this reason and because carfilzomib caused embryo-fetal toxicity in pregnant rabbits at doses lower than the recommended dose, women of child-bearing potential and men must agree to use two effective methods of contraception (hormonal or barrier method of birth control; abstinence) prior to study entry, for the duration of study participation, and 4 months after completion of CB-839 HCl, carfilzomib, and dexamethasone administration. 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. Men treated or enrolled on this protocol must also agree to use adequate contraception prior to the study, for the duration of study participation, and 4 months after completion of CB-839 HCl, carfilzomib, and dexamethasone administration * Ability to understand and the willingness to sign a written informed consent document Exclusion Criteria: * Patients who are refractory or intolerant to carfilzomib (prior carfilzomib exposure accepted) * Patients who have received recent prior chemotherapy with: * Alkylators (e.g., melphalan, cyclophosphamide) and anthracyclines =\< 14 days prior to registration, * High dose corticosteroids and immunomodulatory drugs (thalidomide or lenalidomide) =\< 7 days prior to registration, or * Monoclonal antibodies =\< 14 days prior to registration * Patients who have not recovered from adverse events (AEs) due to prior anti-cancer therapy (i.e., have residual toxicities \> grade 1 except peripheral neuropathy) * Patients who are receiving any other investigational agents * History of allergic reactions attributed to compounds of similar chemical or biologic composition to CB-839 HCl, carfilzomib, or dexamethasone * Patients with uncontrolled intercurrent illness * Any of the following: * Pregnant women or women of reproductive ability who are unwilling to use two effective methods of contraception from the time of signing the informed consent form through 4 months after the last dose of study drug * Nursing women * And men who are unwilling to use birth control while taking the drug and for 4 months after stopping treatment * Pregnant women are excluded from this study because carfilzomib is a PI with the potential for abortifacient effects. Because there is an unknown but potential risk for AEs in nursing infants secondary to treatment of the mother with CB-839 HCl, carfilzomib, and dexamethasone, breastfeeding should be discontinued if the mother is treated with this drug combination * Adverse cardiac history (unstable angina, myocardial infarction less than 4 months, New York Heart Association \[NYHA\] class III or IV congestive heart failure \[CHF\], ejection fraction \[EF\] \< 40%, uncontrolled arrhythmias) * Concomitant high dose corticosteroids other than what is part of treatment protocol (concurrent use of corticosteroids). EXCEPTION: Patients may be on chronic steroids (maximum dose 10 mg/day prednisone equivalent) if they are being given for disorders other than myeloma, e.g., adrenal insufficiency, rheumatoid arthritis, etc * Central nervous system (CNS) involvement * Patients with known brain metastases should be excluded from this clinical trial because of their poor prognosis and because they often develop progressive neurologic dysfunction that would confound the evaluation of neurologic and other AEs * Concurrent amyloid light-chain (AL) amyloidosis * Diagnosed or treated for another malignancy within 2 years before study enrollment or previously diagnosed with another malignancy and have any evidence of residual disease. Patients with nonmelanoma skin cancer or carcinoma in situ of any type are not excluded if they have undergone complete resection * Patient has \>= grade 3 peripheral neuropathy or grade 2 with pain on clinical examination during the screening period * Major surgery within 14 days before study registration * On concurrent treatment with an HIV protease inhibitor * Human immunodeficiency virus (HIV) protease inhibitors can affect the unfolded protein response in myeloma cells as well as the activity of PIs * 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 gastrointestinal (GI) disease or GI procedure that could interfere with the oral absorption or tolerance of CB-839 HCl including difficulty swallowing, refractory vomiting, gastric resection or bypass, or duodenal/jejunal resection