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