Daratumumab After Stem Cell Transplant in Treating Patients With Multiple Myeloma

Inclusion Criteria: * All subjects must have the ability to understand and the willingness to sign a written informed consent * Histologically confirmed diagnosis of multiple myeloma; (patients with multiple myeloma with secondary amyloidosis are eligible) * Received at least two cycles of any regimen as initial systemic therapy for multiple myeloma and are within 2-13 months of the first dose of initial therapy * Eastern Cooperative Oncology Group (ECOG) =\< 2 * Patients with planned standard of care ASCT using melphalan 200 mg/m\^2; dose modifications in accordance with creatinine clearance levels are allowed per physician judgment * Adequate organ function for high dose chemotherapy and autologous stem cell transplant (as per institution standard operating procedure \[SOP\]) * Adequate cell dose \> 2.5 x 10\^6 CD34+ cells/kg * Absolute neutrophil count (ANC) \>= 1000/mm\^3 * Platelet count \>= 75,000/mm\^3; platelet transfusions to help patients meet eligibility criteria are not allowed within 7 days before study enrollment * Total bilirubin =\< 1.5 x the upper limit of normal (ULN) * Aspartate aminotransferase (AST) =\< 3 x ULN * Alanine aminotransferase (ALT) =\< 3 x ULN * Calculated creatinine clearance \>= 30 mL/min * Woman of childbearing potential must be practicing a highly effective method of birth control consistent with local regulations regarding the use of birth control methods for subjects participating in clinical studies: e.g., established use of oral, inje…