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

Inclusion Criteria: * 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study-related procedure not part of normal medical care must be obtained, with the understanding that consent may be withdrawn by the subject at any time without any prejudice to future medical care * Left ventricular ejection fraction \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. Exc…