1. Documentation of pathologic confirmation of a diagnosis of B-Cell acute lymphoblastic leukemia (ALL).
2. TSLPR+ expression must be detected on >=80% of the malignant cells by NSR device. Note: TSLPR+ expression does not need to be repeated by NSR device if there is a documentation of TSLPR surface expression by flow cytometry from a Clinical Laboratory Improvement Amendments (CLIA) approved laboratory.
3. Participants must have a disease that is relapsed or refractory after initial systemic therapy and at least one salvage treatment, and must either be ineligible for, cannot access in a timely manner, or declined alternative curative options (including commercial CAR Tcell constructs\*, and/or have relapsed after allogeneic HSCT).
\*Individuals that are CD19 positive will be considered for this study, However, these individuals should be ineligible for, unable to obtain in a timely manner, cannot access, unwilling to undergo, or have failed prior FDA approved CD19 CAR constructs.
4. Participants must have measurable or evaluable disease at the screening, defined by any evidence of MRD or positron emission tomography (PET)-avid extramedullary disease
5. Age >= 18 years
6. Clinical performance status: Karnofsky >= 50%. Participants who are unable to walk because of paralysis, but who are upright in a wheelchair will be considered ambulatory for the purpose of calculating the performance score.
7. Participants must have adequate organ and marrow function as defined below:
- Leukocytes >= 750/mcL\*
- Platelets >= 50,000/mcL\*
- Total bilirubin <= 2 x upper limit of normal (ULN) (except in the case of participants with documented Gilbert s disease > 3 X ULN)
- Aspartate Aminotransferase (AST)/Alanine Aminotransferase (ALT) <= 5 X institutional ULN
- Creatinine < 1.5X ULN OR Creatinine clearance >= 60 mL/min/1.73m\^2 for participants with creatinine levels above max listed above
- A participant will not be excluded because of pancytopenia >=Grade 3 if it is due to underlying bone marrow involvement by leukemia
8. Cardiac function: left ventricular ejection fraction (LVEF) >=45% or fractional shortening >= 28%, and no clinically significant electrocardiogram (EKG) findings
9. Pulmonary Function: Baseline oxygen saturation > 92% on room air at rest without oxygen supplementation
10. Participants with the following central nervous system (CNS) status are eligible:
- CNS 1, defined as absence of blasts in CSF on cytospin preparation, regardless of the number of WBCs;
- CNS 2, defined as presence of < 5/mcL WBCs in CSF and cytospin positive for blasts, or > 5/mcL WBCs but negative by Steinherz/Bleyer algorithm:
- CNS 2a: < 10/mcL red blood cells (RBCs); < 5/mcL WBCs and cytospin positive for blasts;
- CNS 2b: >=10/mcL RBCs; < 5/mcL WBCs and cytospin positive for blasts;
- CNS 2c: >=10/mcL RBCs; >= 5/mcL WBCs and cytospin positive for blasts but negative by Steinherz/Bleyer algorithm.
11. Contraception:
- Women of child-bearing potential (WOCBP) must agree to use a highly effective contraception (hormonal, intrauterine device \[IUD\], surgical sterilization, abstinence) at the study entry and up to 12 months after the last dose of combined chemotherapy. Note: WOCBP is defined as any individual who has experienced menarche and who has not undergone successful surgical sterilization or who is not postmenopausal.
- Men able to father a child must agree to use an effective method of contraception (barrier, surgical sterilization, abstinence) at the study entry and for 4 months after the last dose of study drugs. We also will recommend men ask their partners to be on highly effective birth control (hormonal, IUD, surgical sterilization). Men able to father a child must not freeze or donate sperm within the same period.
12. Nursing participants must be willing to discontinue nursing from study treatment initiation through 1 month after the last dose of the study drug(s).
13. Ability and willingness of participant or Legally Authorized Representative (LAR) to co-enroll on 15-C-0028: Follow-up Evaluation for Gene-Therapy Related Delayed Adverse Events after Participation in Pediatric Oncology Branch Clinical Trials.
14. Participant or LAR must understand and sign a written informed consent.
EXCLUSION CRITERIA:
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1. Recurrent or refractory leukemia limited to isolated testicular or isolated CNS disease
2. CNS 3 disease including participants with radiologically detected active CNS lymphoma, or participants who have cranial nerve palsy from active CNS leukemia. Note: Chronic complications of prior CNS disease are not exclusionary in the absence of active disease (e.g., blindness from prior ocular CNS disease or persistent cranial nerve palsy)
3. Hyperleukocytosis (>=50,000 blasts/mcL)
4. Positive serum or urine beta-human chorionic gonadotropin (beta-HCG) pregnancy test performed in WOCBP at screening.
5. Washout criteria (time prior to apheresis or prior to start of LD if apheresis is not done on this protocol):
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Therapy: Systemic chemotherapy, antineoplastic investigational agents, or antibody-based therapies, any investigational therapy
Washout\*: >= 2 weeks
Exceptions: 6 weeks for clofarabine or nitrosoureas No washout for prior intrathecal chemotherapy, steroid therapy, hydroxyurea (no dose increases within prior 2 weeks) or ALL maintenance type chemotherapy (vincristine, 6- mercaptopurine, oral methotrexate, or a tyrosine kinase for participants with Ph+ or Ph-like ALL) provided there is recovery from any acute toxic effects.
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Therapy: Radiation therapy
Washout\*: >= 3 weeks
Exceptions: No time restriction with radiation therapy if the volume of bone marrow treated is less than 10% and the participant has measurable/evaluable disease outside the radiation window.
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Therapy: History of allogeneic HSCT
Washout\*: >=100 days since HSCT; >=30 days since completion of immunosuppression; >=6 weeks since donor lymphocyte infusion (DLI)
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Therapy: History of prior CAR therapy or other adoptive cell therapies
Washout\*: > 30 days post infusion
- Time between prior therapy and apheresis or prior to start of LD if apheresis is not done on this protocol.
6. Human immunodeficiency virus (HIV) infection, as measured by seropositivity for HIV antibody.
7. Hepatitis B virus (HBV) infection, as measured by positivity for hepatitis B surface antigen (HbsAg).
8. Hepatitis C virus (HCV) infection, as measured by seropositivity for hepatitis C.
9. Active second malignancy with the exception of in situ carcinoma of the cervix, unless the tumor was treated with curative intent at least two years previously and participant is in remission.
10. History of severe, immediate hypersensitivity reactions attributed to compounds of similar chemical or biologic composition to any agents used in study or in the manufacturing of the cells.
11. Evidence of active graft-versus- host disease (GVHD).
12. Uncontrolled, symptomatic, intercurrent illness or social situations as evaluated by medical history, physical exam, and laboratory evaluations that would limit compliance with study requirements or would pose an unacceptable risk to the participant.