Venetoclax Plus Inotuzumab for B-ALL

Inclusion Criteria: * Participants must have histologically confirmed CD22+ B-ALL or B-LBL. * Note: CD22 must be detected on ≥ 20% of lymphoblasts by flow cytometry of peripheral blood, flow cytometry of bone marrow aspirate or tissue biopsy, or immunohistochemistry of the bone marrow or tissue biopsy. * Note: for R/R disease: ≥ 5% lymphoblasts must be documented in the diagnostic sample (blood, marrow, or tissue biopsy). * Note: Participants with B-LBL (confirmed CD22-positive extramedullary disease, but none or minimal marrow involvement) are eligible if eligibility criteria otherwise met. * Note: Participants with Philadelphia-chromosome positive B-ALL are eligible but must be refractory to 2 or more tyrosine kinase inhibitors (TKIs), refractory to ponatinib, or ineligible to receive all available TKIs. * Note: Participants with chronic myeloid leukemia (CML) in lymphoid blast crisis are eligible but must be refractory to 2 or more TKIs, refractory to ponatinib, or ineligible to receive all available TKIs. * Participants must have disease that is relapsed or refractory (R/R) to 1 or more cycles of cytotoxic chemotherapy. * Note: There is no limit to number or type of prior therapies (prior inotuzumab ozogamicin is not permitted). * Note: Philadelphia-chromosome positive B-ALL patients previously treated with TKI are eligible without receiving cytotoxic chemotherapy if they are unsuitable for standard cytotoxic chemotherapy. * Participants be aged ≥ 18 years. * ECOG performance status of 0-3. * Adequate organ function. * Serum total bilirubin ≤ 1.5x upper limit of normal (ULN), unless due to Gilbert's syndrome or of non-hepatic origin (i.e. hemolysis). * ALT and AST ≤ 2.5x ULN, unless clearly due to disease, in which case ≤ 5x ULN is permissible. * Creatinine clearance of ≥ 30 mL/min calculated using Cockcroft-Gault formula or measured by 24-hour urine collection. * Women of childbearing potential must have a negative serum or urine beta human chorionic gonadotropin (β-hCG) pregnancy test result within 14 days prior to the first dose of study drugs. Women of non-childbearing potential are those who are postmenopausal greater than 1 year or who have had a bilateral tubal ligation or hysterectomy. The effects of venetoclax and inotuzumab ozogamicin on the developing human fetus are unknown. For this reason, women of child-bearing potential and men must agree to use adequate contraception (hormonal or barrier method of birth control; abstinence) prior to study entry, during treatment, and for at least 8 and 5 months after the last dose, respectively. 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. * Human immunodeficiency virus (HIV)-infected participants on effective anti-retroviral therapy with undetectable viral load within 6 months are eligible for this trial. Medication list must be carefully reviewed to ensure no contra-indicated drug-drug interactions. * For participants with known evidence of chronic hepatitis B virus (HBV) infection, the HBV viral load must be confirmed to be undetectable (and appropriate suppressive therapy must be initiated in consultation with an infectious disease expert, if indicated). * Participants with a known history of hepatitis C virus (HCV) infection must have an undetectable HCV viral load confirmed. * Participants with a prior or concurrent malignancy whose natural history or treatment does not have the potential to interfere with the safety or efficacy assessment of the investigational regimen are eligible for this trial. The treating investigator must review such cases with the overall PI prior to confirming eligibility. * Participants with prior HSCT or chimeric antigen receptor T-cell (CAR-T) therapy (autologous or allogeneic) are eligible if they are day +60 from cell infusion and do not have active Glucksberg grade 2 or higher graft versus host disease (GVHD). Patient must be off calcineurin inhibitor for 2 weeks. * Ability to understand and the willingness to sign and date written informed consent document. Exclusion Criteria: * Absolute blast count of ≥25 K/µL prior to initiation of study treatment. Steroids, hydroxyurea, and/or vincristine may be used to reduce blast count. * Prior treatment with inotuzumab ozogamicin at any time. * Prior treatment with venetoclax for relapsed disease; if venetoclax used during first-line therapy, 60 or more days must have elapsed since last dose of venetoclax. Note: The number of patients with prior receipt of venetoclax will be capped at 50% of the participants enrolled in the dose expansion phase. * Treatment for ALL with chemotherapy within 14 days of first dose of study drugs except for hydroxyurea, steroids, vincristine, and/or intra-thecal chemotherapy. * Symptomatic central nervous systemic (CNS) disease and CNS-3 disease. Asymptomatic CNS-2 disease is permitted. Prior CNS disease is not an exclusion. See Appendix B for definition of CNS disease. * Participants with history of decompensated hepatic cirrhosis, veno-occlusive disease (VOD)/sinusoidal obstructive syndrome (SOS), or severe liver disease. * Patient with uncontrolled intercurrent illness, or severe acute or chronic medical or psychiatric condition or laboratory abnormality that in the opinion of the investigator may increase the risk associated with study participation or investigational product administration or may interfere with the interpretation of study results and/or would make the patient inappropriate for enrollment into this study. * Participants who have not recovered from adverse events due to prior anti-cancer therapy (i.e., have residual toxicities \> grade 1) except for alopecia. * Participants who are receiving any other investigational agents. * Participants receiving any medications or substances within 7 days that are strong CYP3A4 inhibitors (such as fluconazole, voriconazole, posaconazole, isavuconazole, and clarithromycin) or inducers (such as rifampin, rifabutin, phenytoin, carbamazepine, and St. John's Wort) of CY3A4 are ineligible. Because the lists of these agents are constantly changing, it is important to regularly consult a frequently updated medical reference (Appendix C). Of note, anti-fungal azole therapy may be re-introduced after venetoclax dose escalation as outlined in the protocol. * Participants who have consumed grapefruit, grapefruit products, Seville oranges (used in marmalade), or star fruit within 3 days prior to starting venetoclax. * Malabsorption syndrome or other conditions (such as inability to swallow pills) that preclude enteral route of venetoclax administration. * Participants with psychiatric illness/social situations that would limit adherence to study requirements. * Pregnant women are excluded from this study because the effects of venetoclax and inotuzumab ozogamicin on the developing human fetus are unknown with the potential for teratogenic or abortifacient effects. There is an unknown but potential risk for adverse events in nursing infants secondary to treatment of the mother with venetoclax and inotuzumab ozogamicin and therefore breastfeeding should be discontinued.