Daratumumab, Pomalidomide, and Dexamethasone in Treating Patients With Relapsed Multiple Myeloma

Inclusion Criteria: * Calculated creatinine clearance (using Cockcroft-Gault equation) \>= 30 mL/min (obtained =\< 14 days prior to registration) * Absolute neutrophil count (ANC) \>= 1000/mm\^3 (obtained =\< 14 days prior to registration) * Untransfused platelet count \>= 75,000/mm\^3 (obtained =\< 14 days prior to registration) * Hemoglobin \>= 8.0 g/dL (obtained =\< 14 days prior to registration) * Total bilirubin =\< 1.5 x upper limit of normal (ULN) (except for patients with Gilbert's syndrome) (obtained =\< 14 days prior to registration) * Alanine aminotransferase (ALT) and aspartate aminotransferase (AST) =\< 2.5 x ULN (obtained =\< 14 days prior to registration) * Measurable disease of multiple myeloma as defined by at least ONE of the following: * Serum monoclonal protein \>= 1.0 g/dL * \>= 200 mg of monoclonal protein in the urine on 24 hour electrophoresis * Serum immunoglobulin free light chain \>= 10 mg/dL AND abnormal serum immunoglobulin kappa to lambda free light chain ratio * Bone marrow \>= 30% plasma cells * Eastern Cooperative Oncology Group (ECOG) performance status (PS) 0, 1 or 2 * Relapsed multiple myeloma (MM) requiring treatment who have previously received a daratumumab alone or in a daratumumab containing combination and * Had at least a partial response to therapy, and had disease progression on or within 60 days of discontinuation * At least 3 months should have elapsed since last exposure to daratumumab * Patients must have been previously exposed to both a proteasome inhibitor and an immunomodulatory imide drug (IMiD) * Examples of proteasome inhibitors: * Bortezomib, carfilzomib, ixazomib, marizomib, oprozomib * Examples of IMiD's: * Thalidomide, lenalidomide, pomalidomide * Negative pregnancy test done =\< 7 days prior to registration, for women of childbearing potential only * Willing to follow strict birth control measures * Female patients: If they are of childbearing potential, agree to one of the following: * Practice 2 effective methods of contraception, at the same time, from the time of signing the informed consent form through 90 days after the last dose of study drug, AND must also adhere to the guidelines of any treatment-specific pregnancy prevention program, if applicable, OR * Agree to practice true abstinence when this is in line with the preferred and usual lifestyle of the subject. (Periodic abstinence \[e.g., calendar, ovulation, symptothermal, post-ovulation methods\] and withdrawal are not acceptable methods of contraception.) * Male patients: even if surgically sterilized (i.e., status post-vasectomy), must agree to one of the following: * Agree to practice effective barrier contraception during the entire study treatment period and through 90 days after the last dose of study drug, OR * Must also adhere to the guidelines of any treatment-specific pregnancy prevention program, if applicable, OR lifestyle of the subject. (Periodic abstinence \[eg, calendar, ovulation, symptothermal, post-ovulation methods\] and withdrawal are not acceptable methods of contraception.) * Willing to follow the requirements of the Pomalyst Risk Evaluation and Mitigation Strategy (REMS) program * Willing to provide bone marrow and blood samples for planned research Exclusion Criteria: * Refractory to pomalidomide * Concurrent amyloid light chain (AL) amyloidosis with organ involvement * Diagnosed or treated for another malignancy =\< 2 years prior to registration or previously diagnosed with another malignancy and have any evidence of residual disease. NOTE: Patients with nonmelanoma skin cancer or carcinoma in situ of any type are not excluded if they have undergone complete resection * Any of the following because this study involves an investigational agent, whose genotoxic, mutagenic and teratogenic effects, on the developing fetus and newborn are unknown: * Pregnant women * Nursing women * Men or women of childbearing potential who are unwilling to employ adequate contraception * Other concurrent chemotherapy, or any ancillary therapy considered investigational. NOTE: Bisphosphonates are considered to be supportive care rather than therapy, and are thus allowed while on protocol treatment * Major surgery =\< 14 days prior to registration * Evidence of current uncontrolled cardiovascular conditions, including hypertension, cardiac arrhythmias, congestive heart failure, unstable angina, or myocardial infarction =\< 6 months. Note: Prior to entry, any electrocardiogram (ECG) abnormality at screening must be documented by the investigator as not medically relevant * Known human immunodeficiency virus (HIV) positive * Known hepatitis B surface antigen-positive status, or known or suspected active hepatitis C infection * Seropositive for human immunodeficiency virus (HIV) * Seropositive for hepatitis B (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 (HBV) 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 (except in the setting of a sustained virologic response \[SVR\], defined as aviremia at least 12 weeks after completion of antiviral therapy) * 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 allergies, hypersensitivity, or intolerance to corticosteroids, monoclonal antibodies or human proteins, or their excipients (refer to respective package inserts or investigator's brochure) or known sensitivity to mammalian-derived products * Known chronic obstructive pulmonary disease with a forced expiratory volume in 1 second (FEV1) \< 50% of predicted normal * Known moderate or severe persistent asthma within the past 2 years or currently has uncontrolled asthma of any classification * Total bilirubin =\< 1.5 x ULN (except for patients with Gilbert's syndrome)