• Pediatric, adolescent, or young adult patients with B-ALL as per NCCN v2.2021 and WHO classification in relapse or primary refractory and, either/both of the following: • Unable to receive anthracyclines (see section 3.1.8) or is PEG-asparaginase intolerant.

‣ For leukemia: Patients must have ≥ 5% blasts expressing CD19 and CD22 in the bone marrow as assessed by morphology or flow cytometry. However, if an adequate bone marrow sample cannot be obtained, patients may be enrolled if there is unequivocal evidence of leukemia with ≥ 5% blasts in the peripheral blood.

⁃ If patient does not have CD20, they can still be enrolled but will not receive rituximab.

• Performance status: Lansky ≥ 50 for patients who are ≤ 16 years old and Karnofsky ≥ 50% for patients who are \> 16 years old.

• Patients with asymptomatic CNS leukemia are eligible (see also Exclusion Criterion 3.2.2.)

• Age \> = 1 years of age and less than 25 years of age.

• The following baseline laboratory data:

‣ Total serum bilirubin ≤1.5x upper limit of normal (ULN). Patients with known Gilbert's syndrome may have a total bilirubin up to ≤3 x ULN.

⁃ Adequate renal function per age51 unless related to the disease. Estimated glomerular filtration rate ≥ 60 mL/min/1.73 m2 based on local institutional practice for age-appropriate determination (eg, Schwartz formula for pediatric patients or Cockcroft Gault formula for adults).

⁃ Alanine aminotransferase (ALT) and/or aspartate aminotransferase (AST) ≤3 x ULN; ≤5 x ULN in case of suspected leukemic liver involvement

• Females 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 and must agree to use one of the following effective contraception methods during the study and 30 days after the last treatment and 8 months after the last dose of inotuzumab and 12 months after the last dose of rituximab. Effective methods of birth control include:

‣ Birth control pills, shots, implants (placed under the skin by a health care provider) or patches (placed on the skin)

⁃ Intrauterine devices (IUDs)

⁃ Condom or occlusive cap (diaphragm or cervical/vault caps) used with Spermicide

⁃ Abstinence

• Males need to inform the doctor right away if the partner becomes pregnant or suspects pregnancy. While in this study and for 30 days after the last treatment the patient should not donate sperm for the purposes of reproduction. He will need to use a condom while in this study and for 30 days after the last treatment and 5 months after the last dose of inotuzumab.

• Patients with cardiac disease, include but not limited to: (Left ventricular ejection fraction (EF) \< 50% (as determined by the Biplane Simpson method) (but not per exclusion criteria 3.2.3.1), or who have received \>450mg/m2 of doxorubicin and cannot receive anthracyclines.