Inclusion Criteria:

          -  Considered transplant eligible

          -  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 Risk Evaluation and Mitigation Strategy
                  (REMS) program

          -  Provide informed written consent

          -  Measurable disease of multiple myeloma at the time specified by one of the following:

               -  If no relapse prior to transplant, values obtained at the time of diagnosis

               -  If disease relapse prior to transplant and the patient did not have treatment for
                  the relapsed disease prior to transplant, the values obtained at the time of
                  relapse immediately prior to the transplant.

               -  If disease relapse prior to transplant and the patient did have treatment for the
                  relapsed disease prior to transplant, the values obtained prior to this therapy,
                  i.e., the time of relapse

        Exclusion Criteria:

          -  Any previous ASCT for multiple myeloma (MM) (NOTE: Patient may have had prior stem
             cell collection before registration on the study)

          -  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 POEMS syndrome (plasma cell dyscrasia with
             polyneuropathy, organomegaly, endocrinopathy, monoclonal protein, and skin changes)

          -  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