Daratumumab in Treating Participants With Relapsed Multiple Myeloma After Stem Cell Transplant

• Patient must have had relapsed disease prior to transplant, or undergone previous autologous stem cell transplant (ASCT), followed by relapse and at least a partial response to salvage therapy
• Eligible patients will be enrolled in the protocol no less than 60 days and must be initiated no longer than 180 (+/- 14) days post autologous stem cell transplantation (ASCT)
• Male or female patients 18 years or older.
• Patients must have an Eastern Cooperative Oncology Group (ECOG) status of 0 to 2

• Patients' clinical laboratory values and toxicity must be as specified below within 14 days before the first dose of the study drug:

  • Platelet count >= 50,000/mm\^3
  • Absolute neutrophil count >= 1000/ mm\^3 (no growth factors within 5 days)
  • Alanine aminotransferase (ALT) and aspartate aminotransferase (AST) \<= 3 x upper limit of normal (ULN)
  • Creatinine \<= 2.5 mg/dL
  • Recovered (i.e., =\< grade 2 toxicity) from the reversible effects of autologous stem cell transplant
• Voluntary written informed consent before performance of any study-related procedure not part of normal medical care must be obtained, with the understanding that consent may be withdrawn by the subject at any time without any prejudice to future medical care
• Left ventricular ejection fraction >/=40% at the patient's last recorded echocardiogram (this could refer to pretransplant ECHO. ECHO may be repeated if the PI considers a repeat ECHO). No uncontrolled arrythmias.

Exclusion Criteria:

• Major surgery within 14 days before the first dose of study drug
• Radiotherapy within 14 days before enrollment
• Non-secretory disease, plasma cell leukemia, or previous allogeneic transplant
• Known active central nervous system involvement
• Inability or unwillingness to comply with the drug administration requirements
• Female subject is pregnant or lactating
• 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 (ie, 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)
• Patients with a known history of asthma or chronic obstructive pulmonary disease with a forced expiratory volume in 1 second (FEV1) \<50% of predicted normal.
• Patients with moderate or severe persistent asthma within the past 2 years and currently uncontrolled asthma of any classification.
• Infection requiring IV systemic antibiotic therapy within 7 days before cycle day 1 (C1D1) of therapy
• Known allergy to any of the study medications, their analogues, or excipients in the various formulations
• Failure to have fully recovered (i.e., \<= grade 2 toxicity) from the effects of prior chemotherapy regardless of the interval since last treatment
• Patient is refractory or resistant to daratumumab and pomalidomide
• Co-morbid systemic illnesses or other severe concurrent disease that, in the judgment of the investigator, would make the patient inappropriate for entry into this study or interfere significantly with the proper assessment of safety and toxicity of the prescribed regimens
• If patient was unable to tolerate daratumumab or pomalidomide in the past