Inclusion Criteria:

          -  Pathologically confirmed diagnosis of multiple myeloma who are transplant eligible and
             have received any prior induction therapy (with or without maintenance)

          -  Measurable MRD in bone marrow within 28 days prior to registration (MPF method)

          -  Eastern Cooperative Oncology Group (ECOG) performance status (PS) 0, 1, or 2 at
             registration

          -  Absolute neutrophil count (ANC) >= 1,000 cell/mm^3 without growth factor support,
             obtained =< 14 days prior to registration

          -  Platelets >= 50,000 cells/mm^3 for patients who have bone marrow plasmacytosis < 50%
             or >= 30,000 cells/mm^3 for patients who have bone marrow plasmacytosis of >= 50%,
             obtained =< 14 days prior to registration

          -  Calculated or measured creatinine clearance >= 30 ml/min, obtained =< 14 days prior to
             registration

          -  Total bilirubin =< 1.5 x upper limit of normal (ULN) unless due to Gilbert?s syndrome,
             in which case the direct bilirubin must be =< 1.5 X ULN, obtained =< 14 days prior to
             registration

          -  Aspartate aminotransferase (AST)/serum glutamic-oxaloacetic transaminase (SGOT) and
             alanine aminotransferase (ALT)/serum glutamic-pyruvic transaminase (SGPT) =< 3 x ULN,
             obtained =< 14 days prior to registration

          -  Prothrombin time (PT)/international normalized ratio (INR) =< 1.5 X ULN, obtained =<
             14 days prior to registration

          -  Negative urine or serum pregnancy test for women of childbearing potential

               -  NOTE: females of reproductive potential must adhere to the scheduled pregnancy
                  testing as required in the Revlimid REMS program

          -  Provide informed written consent

          -  Willing to provide bone marrow aspirate and core, and blood samples for correlative
             research purposes

          -  Measurable disease of multiple myeloma at the time of baseline values for disease
             assessment as defined by at least one of the following:

               -  Serum monoclonal protein >= 1.0 g/dL

               -  >= 200 mg of monoclonal protein in the urine on 24 hour electrophoresis

               -  Serum immunoglobulin free light chain >= 10 mg/dL AND abnormal serum
                  immunoglobulin kappa to lambda free light chain ratio ? Bone marrow plasma cells
                  >= 30%

        Exclusion Criteria:

          -  Any previous ASCT for multiple myeloma (MM)

          -  Any prior therapy with daratumumab

          -  Non-secretory MM or known amyloid light-chain (AL) amyloidosis

          -  Clinically significant active infection requiring intravenous antibiotics (=< 14 days
             prior to registration)

          -  >= grade 3 neuropathy and/or polyneuropathy, organomegaly, endocrinopathy, monoclonal
             protein, skin changes (POEMS syndrome)

          -  Other prior malignancy

               -  Exceptions:

                    -  Adequately treated basal cell or squamous cell skin cancer

                    -  Any in situ cancer

                    -  Adequately treated stage I or II cancer from which the patient is currently
                       in complete remission, or

                    -  Any other cancer from which the patient has been disease free for at least 3
                       years

          -  Concurrent therapy considered investigational

               -  NOTE: patients must not be planning to receive any radiation therapy (except
                  localized radiation for palliative care that must be completed prior to starting
                  cycle 1, day 1)

          -  Pregnant women

          -  Nursing women (lactating females are eligible provided that they agree not to breast
             feed while taking lenalidomide)

          -  Men or women of childbearing potential who are unwilling to employ adequate
             contraception

          -  Major surgery =< 4 weeks prior to registration

          -  History of stroke/intracranial hemorrhage =< 6 months prior to registration

          -  Clinically significant cardiac illness including New York Heart Association (NYHA)
             class III or class IV heart failure, unstable angina pectoris, myocardial infarction
             within the past 6 months, or >= grade 3 cardiac arrhythmias noted =< 14 days prior to
             registration

          -  Known human immunodeficiency virus positive (HIV+) patients

          -  Known hepatitis B or hepatitis C infection

          -  Exhibiting clinical signs of meningeal involvement of multiple myeloma

          -  Known severe chronic obstructive pulmonary disease or asthma defined as forced
             expiratory volume (FEV1) in 1 second less than < 60% of expected