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, injected, or implanted hormonal methods of contraception; placement of an intrauterine device or intrauterine system; barrier methods; condom with spermicidal foam/gel/film/cream/suppository or occlusive cap (diaphragm or cervical/vault caps) with spermicidal foam/gel/film/cream/suppository; male partner sterilization; true abstinence (when this is in line with the preferred and usual lifestyle of the subject) during and after the study (6 months after the last dose of daratumumab for women) * A man who is sexually active with a woman of childbearing potential and has not had a vasectomy must agree to use a barrier method of birth control, e.g., either condom with spermicidal foam/gel/film/cream/suppository or partner with occlusive cap (diaphragm or cervical/vault caps) with spermicidal foam/gel/film/cream/suppository, and all men must also not donate sperm during the study and for 6 months after receiving the last dose of study drug Exclusion Criteria: * Prior disease progression with daratumumab or other anti-CD38 antibody * History of organ or previous autologous/allogeneic stem cell transplantation * Any condition medical or psychosocial that in the opinion of the investigator would hinder compliance * Female patients who are lactating or have a positive pregnancy test during the screening period * Evidence of multiple myeloma (MM) disease progression any time prior to enrollment; progression from smoldering to active myeloma is not exclusionary * History of plasma cell leukemia or central nervous system (CNS) involvement * Major surgery within 14 days prior to start of study treatment * Infection requiring systemic antibiotic therapy within 14 days prior to the start of study treatment * Subject is receiving concurrent chemotherapy or biologic or hormonal therapy for cancer treatment; Note: Concurrent use of hormones for noncancer-related conditions (e.g., insulin for diabetes) is acceptable * Vaccination with live attenuated vaccines within 4 weeks of first study agent administration * Subject is currently using or has used immunosuppressive medication within 14 days prior to the first dose of study treatment; the following are exceptions: * Intranasal, topical, inhaled, or local steroid injections (e.g., intra-articular injection) * Chronic systemic corticosteroids at physiologic doses not to exceed 10 mg/day of prednisone or equivalent * Steroids as premedication for hypersensitivity reaction (e.g., infusion-related reactions, computed tomography \[CT\] scan premedication) * Subject has plasma cell leukemia, Waldenstrom's macroglobulinemia, POEMS syndrome (polyneuropathy, organomegaly, endocrinopathy, monoclonal protein, and skin changes), or primary amyloidosis * Subjects with uncontrolled, systematic infection should be excluded * Subject has known chronic obstructive pulmonary disease (COPD) with a forced expiratory volume in 1 second (FEV1) \< 50% predicted normal; Note that FEV1 testing is required for patients suspected of having COPD and subjects must be excluded if FEV1 \< 50% * Subject has known moderate or severe persistent asthma within 2 years, or currently has uncontrolled asthma of any classification; (Note that subjects who currently have controlled intermittent asthma or controlled mild persistent asthma are allowed in the study) * Subject has active or prior documented autoimmune or inflammatory disorders (including inflammatory bowel disease \[e.g., Crohn's disease\], diverticulitis, celiac disease, irritable bowel disease, or other serious gastrointestinal chronic conditions associated with diarrhea; systemic lupus erythematosus; Wegener syndrome; myasthenia gravis; Graves' disease; rheumatoid arthritis; hypophysitis, uveitis, etc) within the past 3 years prior to the start of treatment; the following are exceptions: * Subjects with vitiligo or alopecia * Subjects with hypothyroidism (e.g., following Hashimoto's disease) stable on hormone replacement * Psoriasis not requiring systemic treatment * Subject has known allergies, hypersensitivity, or intolerance to monoclonal antibodies or human proteins, or their excipients * Subject has history of primary immunodeficiency * Subject is seropositive for human immunodeficiency virus (HIV-1) * Active hepatitis A * 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 finding 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) * Subject has any one of the following: * Clinically significant abnormal electrocardiogram (ECG) finding at screening * Congestive heart failure (New York Heart Association class III or IV) * Myocardial infarction within 12 months prior to starting study treatment * Unstable or poorly controlled angina pectoris, including Prinzmetal variant angina pectoris * Subject has prior history of malignancies, other than MM, unless the subject has been free of the disease for \>= 5 years with the exception of the following malignancies: * Basal cell carcinoma of the skin * Squamous cell carcinoma of the skin * Carcinoma in situ of the cervix * Carcinoma in situ of the breast * Incidental histologic finding of prostate cancer (T1a or T1b using the tumor, node, metastasis \[TNM\] clinical staging system) or prostate cancer that is curative * Any other condition that would, in the opinion of the investigator's judgement, contraindicate the patient's participation in the clinical study due to safety concerns with clinical study procedures * Prospective participants who, in the opinion of the investigator, may not be able to comply with all study procedures (including compliance issues related to feasibility/logistics)