Inotuzumab Ozogamicin Post-Transplant For Acute Lymphocytic Leukemia

Inclusion Criteria: Phase 1 Inclusion Criteria * Diagnosis of CD22-positive Acute Lymphoblastic Leukemia * Patients who underwent an allogeneic hematopoietic stem cell transplantation from any donor source for acute lymphocytic leukemia * Patients who are between T+40 and T+100 after allogeneic transplantation. Patients must receive their first dose of inotuzumab at or before T+100. * Patients who have/are either: * Transplanted in hematologic first complete remission with evidence of minimal residual disease within 45 days of allogeneic transplantation ---Pre- or Post-Transplant Minimal Residual Disease defined by: ----Any detectable ALL (by flow cytometry, cytogenetics, or PCR techniques) as per clinical indication. * In second or third complete remission at the time of allogeneic transplantation * Treated with reduced intensity regimens or non-myeloablative conditioning regimens * Lymphoid blast crisis of CML * Are relapsed or refractory to at least 1 line of chemotherapy * Philadelphia-like ALL * Patients who have evidence of donor chimerism after allogeneic transplantation. * ECOG Performance status \< 2 * Participants must have ANC \> 1,000/µL for 3 days and platelet transfusion independence as defined as a platelet count \> 50,000/µL for 7 days. * Able to adhere to the study visit schedule and other protocol requirements. * Participants must have the ability to understand and the willingness to sign a written informed consent document. Phase 2 Inclusion Criteria * Diagnosis of CD22-positive Acute Lymphoblastic Leukemia * Patients who underwent an allogeneic hematopoietic stem cell transplantation from any donor source for acute lymphocytic leukemia * Patients who are between T+40 and T+100 after allogeneic transplantation * Patients who have/are either: * Transplanted in hematologic first complete remission with evidence of minimal residual disease within 45 days of allogeneic transplantation ---Post-Transplant Minimal Residual Disease defined by: ----Any detectable ALL (by flow cytometry, cytogenetics, or PCR techniques) as per clinical indication. * In second or third complete remission at the time of allogeneic transplantation * Treated with reduced intensity regimens as defined per institutional standard of practice * Lymphoid blast crisis of CML * Are relapsed or refractory to at least 1 line of chemotherapy * Philadelphia-like ALL * Patients who have \> 80% donor chimerism after allogeneic transplantation. * Philadelphia chromosome positive ALL must have failed at least 1 TKI * ECOG Performance status \< 1 * pre-transplant evaluation, see 10.1.1 * Participants must have ANC \> 1,000/µL for 3 days and platelet transfusion independence as defined as a platelet count \> 50,000/µL for 7 days. * Able to adhere to the study visit schedule and other protocol requirements. * Participants must have the ability to understand and the willingness to sign a written informed consent document. Phase 1 and 2 Exclusion Criteria: * Patients with clinical evidence of disease progression prior to enrollment * Persistent prior treatment toxicities Grade 2 and above according to NCI CTCAE Version 4.03 (with the exception for alopecia, neuropathy, etc.) * Patients with inadequate organ function as defined by: * Creatinine clearance \< 30ml/min * Bilirubin \> 2X institutional upper limit of normal * AST (SGOT) \> 2X institutional upper limit of normal * ALT (SGPT) \> 2X institutional upper limit of normal * GVHD grade III or IV (for patients with a prior allogeneic transplant). * Active acute or chronic GVHD of the liver (for patients with a prior allogeneic transplant) * History of VOD * Use of concomitant TKI or sirolimus * Second active malignancy, other than non-melanoma skin cancer or carcinoma in situ (e.g. cervix, bladder, breast) * Patients with uncontrolled inter-current illness including, but not limited to ongoing or active infection, symptomatic congestive heart failure, unstable angina pectoris, cardiac arrhythmia, or psychiatric illness/social situations that would limit compliance with study requirements. * Pregnant or breastfeeding women are excluded from this study because inotuzumab ozogamicin may be associated with the potential for teratogenic or abortifacient effects. Because there is an unknown, but potential risk for adverse events in nursing infants secondary to treatment of the mother with inotuzumab ozogamicin, breastfeeding should be discontinued if the mother is treated with inotuzumab ozogamicin. These potential risks may also apply to other agents used in this study. * Evidence of myelodysplasia or cytogenetic abnormality indicative of myelodysplasia on any bone marrow biopsy prior to initiation of therapy Serologic status reflecting active hepatitis B or C infection. Patients that are positive for hepatitis B core antibody, hepatitis B surface antigen (HBsAg), or hepatitis C antibody must have a negative polymerase chain reaction (PCR) prior to enrollment. (PCR positive patients will be excluded.) * Serologic status reflecting active hepatitis B or C infection. Patients that are positive for hepatitis B core antibody, hepatitis B surface antigen (HBsAg), or hepatitis C antibody must have a negative polymerase chain reaction (PCR) prior to enrollment. (PCR positive patients will be excluded.) * Participation in any other investigational drug study or had exposure to any other investigational agent, device, or procedure, within 21 days (or 5 half-lives, whichever is greater) * Any condition that would, in the investigator's judgment, interfere with full participation in the study, including administration of study drug and attending required study visits; pose a significant risk to the participant; or interfere with interpretation of study data. * Known allergies, hypersensitivity, or intolerance to any of the study medications, excipients, or similar compounds