Inclusion Criteria:

          -  Patients with a diagnosis of Multiple Myeloma who have achieved a VGPR or better
             (based on best response) after induction with or without consolidation therapy/ HDT
             ASCT

          -  MRD positive at screening by flow cytometry

          -  Additionally, patients who were previously MRD negative after induction therapy
             with/without consolidative HDT/ASCT and have turned MRD positive (by flow cytometry)
             based on bone marrow done at screening and do not have any evidence of progressive
             disease are eligible

          -  Patients must be on standard of care lenalidomide maintenance therapy for at least 6
             months at the time of study enrollment

          -  Patient can be receiving bisphosphonate therapy per the treating oncologist's
             discretion

          -  Creatinine clearance ≥45 ml/min using the Cockcroft-Gault method, MDRD, or CKD-EPI
             formula. If the calculated CrCl based on Cockcroft-Gault method, MDRD, or CKD-EPI is
             <45 mL/min, patient will have a 24 hr urine collection to measure CrCl.

          -  Age ≥18 years

          -  Eastern Cooperative Oncology Group (ECOG) performance status 0-2

          -  Male or female patient who accepts and is able to use recognized effective
             contraception (oral contraceptives, IUCD, barrier method of contraception in
             conjunction with spermicidal jelly) throughout the study when relevant.

          -  Absolute neutrophil count (ANC) ≥1.0 x 10^9/L, hemoglobin ≥8 g/dL, and platelet count
             ≥75 x 10^9/L. No transfusion or growth factor support for one week prior to labs.

          -  Adequate hepatic function, with bilirubin < 1.5 x the ULN, and AST and ALT < 2.5 x ULN

        Exclusion Criteria:

          -  Patients with a diagnosis of MM not achieving a VGPR or better to the most recent
             therapy.

          -  Patients with a diagnosis of MM who are MRD Negative by flow cytometry

          -  Patients must not have measurable disease at the time of enrollment. Measurable
             disease is defined as follows

               -  Serum monoclonal protein > 0.5 gm/dL

               -  Urine monoclonal protein > 200 mg/24 hours

               -  Involved serum free light chain > 10 mg/dL

          -  Pregnant or lactating females

          -  Uncontrolled hypertension or diabetes

          -  Has significant cardiovascular disease with NYHA Class III or IV symptoms, or
             hypertrophic cardiomegaly, or restrictive cardiomegaly, or myocardial infarction
             within 3 months prior to enrollment, or unstable angina, or unstable arrhythmia

          -  Uncontrolled intercurrent illness including but not limited to active infection or
             psychiatric illness/social situations that would compromise compliance of study
             requirements

          -  Active infection requiring treatment within two weeks prior to first dose

          -  Contraindication to any concomitant medication, including antivirals, anticoagulation
             prophylaxis, tumor lysis prophylaxis, or hydration given prior to therapy

          -  Major surgery within 1 month prior to enrollment

          -  Previous therapy with daratumumab or other anti-CD38 monoclonal antibodies

          -  History of other malignancy (apart from basal cell carcinoma of the skin, or in situ
             cervix carcinoma) except if the patient has been free of symptoms and without active
             therapy during at least 5 years

          -  Active hepatitis B or C infection

          -  Subject is:

               -  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) 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).