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

Inclusion Criteria: * Participant or legally authorized representative (LAR) must provide written informed consent before any study specific procedures or interventions are performed * Participants must be \>= 18 years of age * Histologically or cytologically confirmed diagnosis of multiple myeloma (MM) as defined by 2016 International Myeloma Working Group (IMWG) criteria * Relapsed or relapsed and refractory (R/R) MM, as defined by International Myeloma Working Group (IMWG) criteria: * Relapsed myeloma: Previously treated myeloma that has progressed and is neither "refractory myeloma" nor "relapsed-and-refractory myeloma" * Refractory myeloma: Nonresponsive myeloma while on primary or salvage therapy, or progresses within 60 days of last therapy. Nonresponsive disease is defined as failure to achieve minimal response (MR) or better, achieved with any therapy. Cases in which there is no significant change in M protein and no evidence of clinical progression, are included, as well those cases that progress in disease course * Primary refractory myeloma: Disease that is nonresponsive in patients who have never achieved a minimal response or better with any therapy * Relapsed-and-refractory myeloma: Disease that is nonresponsive while on salvage therapy or progresses with 60 days of last therapy after achieving MR or better previously before progressing * Participant has received at least 1 line of prior therapy. * Prior exposure to proteasome inhibitor is permitted. The washout period is 2 weeks (14 days) prior to start of study treatment (cycle 1 day 1 \[C1D1\]) * Prior exposure to immunomodulatory imide drug (IMiD) therapy (lenalidomide, pomalidomide, or thalidomide) is permitted. The washout period is 2 weeks (14 days) prior to start of study treatment (C1D1) * Prior treatment with anti-CD38 therapy (e.g., daratumumab) is permitted. The washout period is 6 months prior to start of study treatment (C1D1) * Measurable disease with at least one of the following: * Monoclonal immunoglobulin spike on serum protein electrophoresis of \>= 0.5 g/dL * Urine monoclonal immunoglobulin spike of \>= 200 mg/24 hours * Involved free light chain (FLC) \>= 10 mg/dL and an abnormal serum FLC ratio (i.e., \< 0.26 or \> 1.65) * Eastern Cooperative Oncology Group (ECOG) performance status =\< 2 (Karnofsky \>= 50%) * Toxicity related to prior therapies that, in the opinion of the investigator, would potentially be worsened with anti-CD38 therapy should be resolved to baseline or less than grade 1 * Anticipated life expectancy of at least 6 months (per investigator discretion) * No contraindication to receiving thromboprophylaxis for pomalidomide * Patients must have normal marrow and organ function as defined by: * Absolute neutrophil count (ANC) ≥ 1,000/uL. Patients may receive growth factor support to meet screening criteria. Screening ANC must be redrawn 72 hours after growth factor dosing. Screening platelets or hemoglobin must be redrawn 72 hours after transfusion * Platelets \>= 75,000/uL within 14 days prior to registration. Patients may have received transfusion if \> 7 days prior to registration * Hemoglobin concentration of \>= 8.0 g/dL within 14 days prior to registration. Patients may have received transfusion if greater than 7 days prior to registration * Must have adequate liver function, as defined by: * Normal total bilirubin (as per institutional upper limits of normal \[IULN\]), except if due to Gilbert's syndrome, or other documented historical elevations in serum bilirubin levels, at the discretion of the investigator, AND * Aspartate aminotransferase (AST) (serum glutamic oxaloacetic transaminase \[SGOT\])/alanine aminotransferase (ALT) (serum glutamic pyruvic transaminase \[SGPT\]) =\< 2 x IULN * Must have adequate renal function, as defined by: * Creatinine clearance (CrCl) of \>= 30 mL/min, as measured by a 24-hour urine collection or as estimated by the Cockcroft and Gault formula. The serum creatinine value used in the calculation must have been obtained within 35 days prior to registration. * For patients with a creatinine clearance within the range of 30-45 mL/min, stability (i.e., not deteriorating) must be demonstrated over a period of 8 weeks prior to enrollment in the study * Lab parameters must continue to be met at the time of registration. If parameters not met at the intended C1D1, transfusion or growth factor support may be considered in consultation with the team, if the individual is still within the screening window * Left ventricular ejection fraction (LVEF) by echocardiogram \>= 40%. The echocardiogram study should be obtained during screening or up to 60 days prior to consent * Women of childbearing potential must have a negative serum or urine pregnancy test within 14 days prior to receiving the first dose of study medication. If the urine pregnancy test is positive or cannot be confirmed as negative, a serum pregnancy test will be required * Female participants of childbearing potential (FOCBP) must agree to use highly-effective method(s) of contraception during the study and for 3 months after the last dose of study drug. FOCBP are those who have not been surgically sterilized or have not been free from menses for \> 1 year without an alternative medical cause * Male participants must agree to use an adequate method of contraception starting with the first dose of study therapy through 3 months after the last dose of study drug Exclusion Criteria: * Waldenstrom macroglobulinemia * Multiple myeloma of immunoglobulin M (IgM) subtype * POEMS syndrome (polyneuropathy, organomegaly, endocrinopathy, monoclonal protein, and skin changes) * Plasma cell leukemia (\> 2.0 x 10\^9/L circulating plasma cells by standard differential) * Myelodysplastic syndrome * Participants with known or suspected amyloidosis * Individuals that are refractory to prior treatment with either carfilzomib or pomalidomide * Intolerance leading to discontinuation of either carfilzomib or pomalidomide * Prior allogeneic stem cell transplant * Second malignancy requiring concurrent treatment or those with non-hematological malignancies (except non-melanoma skin cancers). Cancer treated with curative intent \< 5 years previously will not be allowed unless approved by the principal investigator (PI). Cancer treated with curative intent \> 5 years previously is allowed * Any known allergies or hypersensitivity to isatuximab or other monoclonal antibody therapies and required premedications * Known history of allergy to Captisol (a cyclodextrin derivative used to solubilize carfilzomib) * Hypersensitivity to any of the components of study therapy that is not amenable to premedication with steroids and H2 blockers * Participant has received prior chemotherapy, targeted small molecule therapy, or radiation therapy within 2 weeks or 5 pharmacokinetic half-lives of the treatment, whichever is longer, of the first dose of study medication. Wash-out period of prior anti-CD38 therapy (e.g. Daratumumab) is 6 months before first dose of study medication. * Exception: Emergency use of a short course of corticosteroids (equivalent of dexamethasone 40 mg per day for a maximum of 4 days) before treatment is not a barrier to eligibility * Participant has undergone autologous stem cell transplant within 90 days of the first dose of study medication * Ongoing adverse events related to a previously administered anti-myeloma therapy (including radiation therapy) \>= grade 1 * Exception: Potential participants with =\< grade 2 neuropathy may, at the discretion of the investigator, qualify for the study * Active autoimmune disease, except vitiligo or hypothyroidism * Active and ongoing steroid use, except for non-systemically absorbed treatments (such as inhaled or topical steroid therapy for asthma, chronic obstructive pulmonary disease \[COPD\], allergic rhinitis, or dermatologic conditions) and the emergency use of corticosteroids outlined above * Known human immunodeficiency virus (HIV) infection * Ongoing or active systemic infection * Seropositive for hepatitis B virus (HBV) defined by a positive test for hepatitis B surface antigen (HBsAg). Subjects with resolved infection (i.e., subjects who are HBsAg negative but positive for antibodies to hepatitis B core antigen \[anti-HBc\] and/or antibodies to hepatitis B surface antigen \[anti-HBs\]) must be screened using real-time polymerase chain reaction (PCR) measurement of hepatitis B virus deoxyribonucleic acid (DNA) levels. Those who are PCR positive will be excluded. Exception: Subjects with serologic findings suggestive of HBV vaccination (anti-HBs positivity as the only serologic marker) AND a known history of prior HBV vaccination, do not need to be tested for HBV DNA by PCR * Seropositive for hepatitis C virus (HCV) (except in the setting of a sustained virologic response, defined as aviremia at least 12 weeks after completion of antiviral therapy) * Evidence of current uncontrolled cardiovascular conditions, including uncontrolled hypertension, uncontrolled cardiac arrhythmias, symptomatic congestive heart failure (New York Heart Association \[NYHA\] Class III or IV), pulmonary hypertension, unstable angina, or myocardial infarction within the past 6 months * Participant has received a live vaccine within 30 days of planned start of study therapy * A history of non-infectious pneumonitis that required treatment with steroids, or current pneumonitis * Diagnosis of immunodeficiency or treatment with any form of immunosuppressive therapy within 7 days prior to the first dose of study medication * Pregnant or breastfeeding * Any medical or psychiatric conditions that in the opinion of the PI would preclude safe participation in protocol