Inclusion Criteria:

          -  Eastern Cooperative Oncology Group performance status between 0-2

          -  Serum creatinine =< 1.5 x upper limit of normal (ULN) or calculated creatinine
             clearance (Cockcroft and Gault) > 30 mL/min

          -  Alanine aminotransferase (ALT) =< 5 x ULN

          -  Total bilirubin= < 1.5 x ULN

          -  Left ventricular ejection fraction (LVEF) >= 40% as assessed by echocardiogram (ECHO)
             or multiple-gated acquisition (MUGA) scan performed within 28 days of enrollment

          -  Diagnosis of relapsed/refractory CD22+ B-cell ALL with disease in the bone marrow
             and/or peripheral blood by morphology (>=5% blasts). CD22-positive B-ALL is defined as
             expression by at least 20% of malignant lymphoblasts as determined by local flow
             cytometry and/or immunohistochemistry from a peripheral blood and/or bone marrow
             sample obtained within 2 weeks of screening

          -  Relapsed or refractory disease, defined as second or greater bone marrow relapse from
             CR or overall response or, disease has progressed following two or more anti-leukemia
             therapies. Specifically:

               -  Any bone marrow relapse after allogeneic HSCT: subjects must be at least 1 month
                  from HSCT at the time of screening and off immunosuppressive medication for at
                  least 2 weeks at time of initial treatment (with the exception of low-dose
                  steroids =< 20 mg prednisone equivalent) and have no active graft versus (vs.)
                  host disease (GVHD);

               -  Philadelphia chromosome (Ph) negative B-ALL which has not achieved CR or CRi
                  after at least 2 attempts at remission induction using standard intensive
                  chemotherapy regimen(s);

               -  Philadelphia chromosome (Ph) positive B-cell ALL intolerant to or ineligible for
                  BCR-ABL tyrosine kinase inhibitor (TKI) therapy or with disease which has
                  progressed after at least two lines of prior TKI therapy

          -  Participants of childbearing potential must agree to use adequate contraceptive
             methods (e.g., hormonal or barrier method of birth control; abstinence) prior to study
             entry and for females, at least 8 months after the final dose of inotuzumab
             ozogamicin. Males with female partners of childbearing potential must agree to use
             adequate contraceptive prior to study entry and for at least 5 months after the final
             dose of inotuzumab ozogamicin. Should a woman become pregnant or suspect she is
             pregnant while she or her partner is participating in this study, she should inform
             her treating physician immediately

          -  Participant or legal representative must understand the investigational nature of this
             study and sign an Independent Ethics Committee/Institutional Review Board approved
             written informed consent form prior to receiving any study related procedure

        Exclusion Criteria:

          -  Receipt of chemotherapy, radiotherapy, or investigational drug therapy within 2 weeks
             prior to treatment on study or those who have not recovered from adverse events due to
             agents administered > 2 weeks earlier

          -  Participants on oral or injectable calcineurin inhibitors (e.g., cyclosporin,
             tacrolimus) within 4 weeks prior to study enrollment

               -  Active central nervous system involvement; patients who have a history of central
                  nervous system (CNS) disease which has been effectively treated (as defined by at
                  least one negative cerebrospinal sample prior to screening) are eligible

          -  Prior malignancy, unless treated with curative intent and with no evidence of active
             disease present for > 5 years before screening, with the following exceptions:

               -  Subjects with stage I breast cancer that has been completely and successfully
                  treated, requiring no therapy or only anti-hormonal therapy

               -  Subjects with T1N0M0 or T2N0M0 colorectal cancer who have been completely and
                  successfully resected and who are disease-free for > 2 years prior to screening

               -  Subjects with indolent prostate cancer, defined as clinical stage T1 or T2a,
                  Gleason score =< 6, and prostate-specific antigen (PSA) < 10 ng/mL, requiring no
                  therapy or only anti-hormonal therapy

               -  Subjects with a history of basal cell or squamous cell carcinoma of the skin, or
                  carcinoma in situ of the cervix, fully resected, and with no evidence of active
                  disease

          -  Uncontrolled intercurrent medical illness including, but not limited to, symptomatic
             congestive heart failure, unstable angina pectoris, cardiac arrhythmia, or psychiatric
             illness/social situations that in the opinion of the investigator would limit
             compliance with study requirements

          -  Uncontrolled systemic fungal, bacterial, viral, or other infection defined as
             exhibiting ongoing signs and symptoms due to infection despite appropriate
             anti-infective therapy at time of screening

          -  Pregnant or nursing female participants

          -  Active hepatitis B, active hepatitis C, or any human immunodeficiency virus (HIV)
             infection at the time of screening

          -  Presence of grade II-IV acute or extensive chronic graft versus host disease (GVHD) at
             time of screening

          -  Unwilling or unable to follow protocol requirements

          -  Any condition which in the investigator's opinion deems the participant an unsuitable
             candidate to receive study drug including, but not limited to, medical, psychological,
             familial, social, or geographical considerations