Inclusion Criteria:

          -  Patients with B-lineage ALL in hematologic complete remission (CR) with molecular
             failure (i.e., had never achieved an MRD-negativity status before inotuzumab
             ozogamicin) or had a molecular relapse (i.e., became MRD positive after having been
             MRD negative) starting at any time point after 3 months of frontline therapy.
             Molecular disease or minimal residual disease is defined by a value of at least of
             10^-4 (0.01%) by multicolor flow cytometry, PCR and/or next-generation sequencing
             (NGS).

          -  Patients with B-lineage ALL in at least marrow CR in salvage 1 and beyond with MRD
             failure at any time point after 1 month of salvage therapy are allowed, including
             patients who received prior allogeneic stem cell transplantation.

          -  Patients with Philadelphia chromosome (Ph)+ ALL can be enrolled in CR1 or CR2 and
             beyond. A tyrosine kinase inhibitor (TKI) will be added at the discretion of the
             treating physician. MRD for these patients will be defined by either 1.) a ratio of
             BCR-ABL1 to ABL1 by PCR of 0.01% according to the international scale for patients
             with p210 transcript or a ratio of BCR-ABL1 to ABL1 by PCR of 0.01% for patients with
             non-p210 transcripts, or 2.) detectable MRD at a level of at least 1x10^-4 (0.01%) by
             multicolor flow cytometry and/or by NGS.

          -  Performance status of 0, 1, or 2

          -  Creatinine clearance >= 15 ml/min

          -  Bilirubin < 1.5 X upper limit of normal (ULN)

          -  Aspartate aminotransferase (AST) or alanine aminotransferase (ALT) < 3 X ULN

          -  No active or co-existing malignancy with life expectancy less than 12 months

        Exclusion Criteria:

          -  Pregnant or nursing women

          -  Known to be human immunodeficiency virus positive (HIV+)

          -  Active and uncontrolled disease/infection as judged by the treating physician

          -  Unable or unwilling to sign the consent form

          -  Active central nervous system (CNS) or extramedullary disease

          -  Monoclonal antibodies therapy within 2 weeks before study entry

          -  Radiotherapy or cancer chemotherapy (except for intrathecal prophylaxis and/or
             low-dose maintenance therapy such as vinca alkaloids, mercaptopurine, methotrexate,
             steroids) or any investigational drug within 2 weeks before study entry