Study Of KITE-753 in R/R B-Cell ALL

Inclusion Criteria: * Patients ≥18 years of age with relapsed and/or refractory B-cell ALL after 1 or more lines of therapy with ≥5% and \<75% bone marrow blasts at the time of consent * Blasts should be positive (≥1%) for either CD19 or CD20 as assessed by flow-cytometry or positive for either CD19 or CD20 by immunohistochemistry * Patients with Philadelphia chromosome-positive ALL are eligible if they are intolerant or have failed 2 lines of any TKI or one line of second-generation TKI * ECOG performance status ≤2 * Adequate organ function: Creatinine clearance \>50 ml/min, direct bilirubin ≤1.5 mg/dL, AST/ALT ≤5.0 x ULN (except in patients with leukemia involvement where up to 10 x ULN is allowed), left ventricular ejection fraction \>40% * The effects of KITE-753 on the developing human fetus are unknown. For this reason and because chemotherapy used in this trial is known to be teratogenic, women of childbearing potential (WOCBP) and men must agree to use adequate contraception (hormonal or barrier method of birth control; abstinence) prior to study entry and for at least 12 months after the last dose of study treatment. This includes all female patients, between the onset of menses (as early as 8 years of age) and 55 years unless the patient presents with an applicable exclusionary factor which may be one of the following: * Postmenopausal (no menses in greater than or equal to 12 consecutive months). * History of hysterectomy or bilateral salpingo-oophorectomy. * Ovarian failure (Follicle Stimulating Hormone and Estradiol in menopausal range, who have received Whole Pelvic Radiation Therapy). * History of bilateral tubal ligation or another surgical sterilization procedure. * Approved methods of birth control are as follows: Hormonal contraception (i.e. birth control pills, injection, implant, transdermal patch, vaginal ring), Intrauterine device (IUD), Tubal Ligation or hysterectomy, Subject/Partner post vasectomy, Implantable or injectable contraceptives, and condoms plus spermicide. Not engaging in sexual activity for the total duration of the trial and the drug washout period is an acceptable practice; however periodic abstinence, the rhythm method, and the withdrawal method are not acceptable methods of birth control. 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. * Men treated or enrolled on this protocol must also agree to use adequate contraception prior to the study, for the duration of study participation, and 12 months after the last dose of study treatment. * Ability to understand and willingness to sign a written informed consent document * For patients with evidence of chronic hepatitis B virus (HBV) infection, the HBV viral load must be undetectable on suppressive therapy, if indicated. * Patients with a history of hepatitis C virus (HCV) infection must have been treated and cured. For patients with HCV infection who are currently on treatment, they are eligible if they have an undetectable HCV viral load. Exclusion Criteria: * Patients who have received prior CAR T-cell therapy or other cell therapies * History of CTCAE grade 4 neurologic event or grade 4 CRS (Lee 2014 criteria) with prior CD19-directed therapy * Presence or suspicion of fungal, bacterial, viral, or other infection that is uncontrolled or requires IV antimicrobials for management Note: Simple urinary tract infections and uncomplicated bacterial or viral upper respiratory tract infections are permitted if the participant is responding to active treatment and satisfies the criteria of being afebrile for 48 hours (i.e., temperature \< 38°C). * Symptomatic CNS disease (i.e. cranial nerve palsies) at the time of enrollment. Patients could have prior history of CNS disease but no symptomatic CNS disease at the time of study enrollment. * Presence of CNS-3 disease (defined as detectable cerebrospinal blast cells in a sample of CSF with ≥ 5 WBCs per mm3) with or without neurological changes, and presence of CNS-2 disease (defined as detectable cerebrospinal blast cells in a sample of CSF with \<5 WBCs per mm3) with neurological changes Note: Subjects with CNS-1 (no detectable leukemia in the CSF) and those with CNS-2 without clinically evident neurological changes are eligible to participate in the study. * History or presence of clinically relevant CNS pathology or event such as epilepsy, childhood or adult seizure, paresis, aphasia, stroke, severe brain injuries, dementia (grade 2 or higher memory impairment per CTCAEv5.0), Parkinson's disease, cerebellar disease, organic brain syndrome, psychosis or severe (grade ≥3) CNS events including ICANS from T cell engager therapies. * Acute or chronic GVHD requiring systemic treatment within 4 weeks prior to enrollment * Diagnosis of Burkitt's leukemia/lymphoma according to WHO classification or chronic myelogenous leukemia lymphoid blast crisis * Current uncontrolled autoimmune disease * History of Hemophagocytic lymphohistiocytosis / Macrophage activation syndrome * Prior medication: * Salvage systemic therapy (including chemotherapy, TKIs for Ph+ ALL, and blinatumomab) within 1 week or 5 half-lives (whichever is shorter) prior to enrollment * Treatment with alemtuzumab within 6 months prior to enrollment, clofarabine or cladribine within 3 months prior to enrollment, or PEG-asparaginase within 3 weeks prior to enrollment * Donor lymphocyte infusion (DLI) within 28 days prior to enrollment * Any drug used for GVHD within 4 weeks prior to enrollment (e.g., calcineurin inhibitors, methotrexate, mycophenolate, rapamycin, thalidomide), or immunosuppressive antibody used within 4 weeks prior to enrollment (e.g., antiCD20, anti-tumor necrosis factor, anti-interleukin 6 or anti-interleukin 6 receptor) * Corticosteroid therapy at a pharmacologic dose (\>5 mg/day of prednisone or equivalent doses of other corticosteroids) and other immunosuppressive drugs must be avoided for 7 days prior to enrollment * Patients with psychiatric illness/social situations that would limit compliance with study requirements * Patients unable/unwilling to sign informed consent form * Because no dosing or adverse event data are currently available on the use of KITE-753 in patients \<18 years of age, children are excluded from this study * Human Immunodeficiency Virus (HIV)-positive unless taking appropriate anti-HIV medications, having an undetectable viral load by qPCR, and a CD4 count ≥200 cells/µL * Pregnant women are excluded from this study. Because there is an unknown but potential risk for adverse events in nursing infants, secondary to treatment of the mother with KITE753, breastfeeding should be discontinued if the mother is treated with KITE-753 * WOCBP must have a negative pregnancy test. WOCBP defined as not post-menopausal for 12 months or no previous surgical sterilization * Patients of either sex who are not willing to practice highly effective birth control from the time of informed consent through 12 months after lymphodepleting chemotherapy or the KITE-753 administration, whichever is longer