Isatuximab, Carfilzomib, Pomalidomide, and Dexamethasone for the Treatment of Relapsed or Refractory Multiple Myeloma

Inclusion Criteria: * Patients with relapsed or refractory multiple myeloma, with \>= 1 prior therapy * Must have received prior lenalidomide therapy * Must have measurable disease, as defined by International Myeloma Working Group criteria, having one or more of the following: * Serum M protein \>= 0.5 g/dL * Urine M protein \>= 200 mg/24 hours * Involved serum free light chain level \>= 10 mg/dL with abnormal kappa/lambda ratio * Measurable biopsy-proven plasmacytomas (\>= 1 lesion has a single diameter \>= 2 cm) * Bone marrow plasma cells \>= 30% * Age 18 years and older, and have the capacity to give informed consent * Eastern Cooperative Oncology Group (ECOG) performance status of 0-2 * Subjects should have resolution of any toxicities from prior therapy to grade =\< 1 or baseline prior to enrollment (with the exception of peripheral neuropathy) * Subjects are required to have grade =\< 2 peripheral neuropathy to enroll * Prior autologous stem cell transplant is allowed; patients must be \>= 6 months post- autologous stem cell transplantation to enroll * Estimated glomerular filtration rate (eGFR) \>= 20 ml/min * Alanine aminotransferase (ALT) and aspartate aminotransferase (AST) =\< 3 x upper limit of normal (ULN) * Total bilirubin =\< 2 x ULN * Absolute neutrophil count (ANC) \>= 1,000/uL * Platelets \>= 50,000/uL * Hemoglobin \>= 8 g/dL * Growth factor use or transfusions may be used to meet the eligibility requirement for ANC, platelets, and hemoglobin * Female patients of childbearing potential and male patients must agree to use 2 effective forms of contraception or continuously abstain from heterosexual intercourse during the period of therapy, and for 6 months after discontinuation of study treatment for females and 3 months after discontinuation of study treatment for males Exclusion Criteria: * History of clinically significant cardiovascular disease, including congestive heart failure New York Heart Association (NYHA) class 3-4, symptomatic ischemia, left ventricular ejection fraction \< 40%, uncontrolled conduction abnormalities, myocardial infarction in last 6 months * Uncontrolled hypertension as determined by the principal investigator (PI) or designee * Active plasma cell leukemia or systemic amyloid light-chain (AL) amyloidosis * History of another primary malignancy that has not been in remission for at least 1 year * However, the following diagnoses are eligible for inclusion: non-melanoma skin cancer, localized prostate cancer, superficial bladder cancer, cervical carcinoma in situ, on biopsy or any prior malignancy with an estimated \> 90% 1-year cure rate per sponsor-investigator * For patients with chronic hepatitis B viral infection, the hepatitis B virus (HBV) polymerase chain reaction (PCR) must be undetectable on suppressive therapy * Patients with a history of Hepatitis C viral infection must have been treated and cured. For patients on treatment for hepatitis C, they are eligible if they have an undetectable hepatitis C virus (HCV) viral load * Subjects with active uncontrolled infection * Concurrent use of other anticancer agents or experimental treatments