A Study of Ponatinib With Chemotherapy in Children, Teenagers, and Adults With Philadelphia Chromosome-Positive Acute Lymphoblastic Leukemia

Inclusion Criteria: 1. Participants must have a diagnosis of Ph+ ALL, Philadelphia chromosome-positive plus mixed phenotype acute leukemia (Ph+ MPAL), or Ph-like ALL with: a) Involvement of BM with ALL, including one of the following: i. M2 BM (5%-24% lymphoblasts): by morphology with confirmatory testing consisting of at least one of the following: flow cytometry lymphoblasts ≥5%, or BCR-ABL1 fluorescence in situ hybridization, or ≥10-2 leukemic clone identified by immunoglobulin heavy chain-T-cell receptor polymerase chain reaction, OR ii. M3 BM (≥25% lymphoblasts): by morphology, OR iii. Participants with combined BM (as defined above) and extramedullary disease. b) Evidence of Ph+ ALL, MPAL, or Ph-like ALL: i. Definite evidence of BCR-ABL1 fusion (Ph) for Ph+ ALL and MPAL, OR ii. Definite evidence of Ph-like ALL with targetable kinase-activating lesions involving any of the following kinase genes: ABL1, ABL2, CSF1R, and PDGFRB. Ph-like ALL diagnosis requires the identification of specified targetable kinase-activating lesions preferably by ribonucleic acid (RNA) sequencing or by alternative accredited method used by the site. c) Disease status: (i) For non-US sites: participants who have relapsed (post 0 or 1 HSCT) or are resistant or intolerant to at least one prior therapy that contained a BCR-ABL-targeted tyrosine kinase inhibitor (TKI), or for US sites: participants who have relapsed (post 0 or 1 HSCT) or are resistant or intolerant to at least one prior therapy that contained a second-generation BCR-ABL1-targeted TKI (i.e, dasatinib, nilotinib, and bosutinib); OR (ii) Have a BCR-ABL1 T315I mutation irrespective of relapse, resistance/intolerance, or transplant status and irrespective of any prior TKI use. Notes: A participant will be defined as intolerant if they had a Grade ≥3 nonhematologic toxicity or a Grade 4 hematologic toxicity considered related to the last TKI and lasting for \>2 weeks, and led to discontinuation of therapy. 2. Weight: Participants must be weighing at least 5 kg at the time of enrollment. 3. Performance Status: Karnofsky performance status ≥50% for participants ≥16 years of age or Lansky Play Scale ≥50% for participants \<16 years of age. 4. Have recovered to less than Grade 2 National Cancer Institute common terminology criteria for adverse events (NCI CTCAE) Version 5.0, or to baseline, from any nonhematologic toxicities (except alopecia) due to previous therapy. 5. Participants must meet the following criteria related to prior therapies: * Cytoreduction with hydroxyurea: Hydroxyurea can be initiated and continued for up to 24 hours before the start of protocol therapy. * Participants who relapsed while receiving cytotoxic therapy: At least 14 days must have passed since the completion of the last dose of chemotherapy before the first dose of ponatinib can be given except for the following: intrathecal (IT) chemotherapy and/or maintenance therapy such as vincristine, mercaptopurine, methotrexate, or glucocorticoids. There is no waiting period for those relapsing on maintenance-like therapy. * HSCT: Participants who have experienced relapse after a HSCT are eligible, provided they have no evidence of acute or chronic graft-versus-host disease (GVHD), are not receiving GVHD prophylaxis or treatment, and are at least 90 days posttransplant at the time of enrollment. * Hematopoietic growth factors: Before the first dose of ponatinib, at least 7 days must have passed since completion of therapy with granulocyte colony-stimulating factor or other growth factors, and at least 14 days must have passed since completion of therapy with pegfilgrastim. * Biologics and targeted therapies: Before the first dose of ponatinib, at least 7 days must have passed since the last dose of a biologic agent. For agents that have known AEs occurring beyond 7 days after administration, this period must be extended beyond the time during which AEs are known to occur. The duration of this interval must be discussed with the sponsor's medical monitor/designee. * Monoclonal antibodies: After the last dose of monoclonal antibody, at least 3 half-lives of the administered antibody must have passed before the first dose of ponatinib. * Immunotherapy: Before the first dose of ponatinib, at least 30 days must have passed after the completion of any type of immunotherapy (eg, tumor vaccines, chimeric antigen receptor T-cell \[CAR-T-cell\]). * Immunosuppressive therapy: Before the first dose of ponatinib, at least 14 days must have passed after the completion of immunosuppressive therapy (including regimens following stem cell transplant). * Radiotherapy: No washout period is necessary for radiation given to any extramedullary site other than central nervous system (CNS); ≥90 days must have passed if participant received prior total body irradiation or craniospinal or cranial radiotherapy. * Anthracyclines: Participants must have had a lifetime exposure of \<400 milligrams per square meter (mg/m\^2) of doxorubicin equivalents of anthracyclines. 6. a) Adequate renal function defined as: Estimated glomerular filtration rate (eGFR) using the Schwartz formula, OR radioisotope glomerular filtration rate (GFR)≥70 mL/min/1.73 m\^2, OR a normal serum creatinine based on age and sex. b) Adequate liver function defined as: Direct bilirubin ≤1.5 times the upper limit of normal (ULN) for age AND ALT ≤5 times the ULN for age. 7. No clinical, radiological or laboratory evidence of pancreatitis, including: 1. Serum lipase must be \<2 times the ULN, AND 2. Serum amylase must be \<2 times the ULN. 8. Adequate cardiac function defined as shortening fraction ≥27% by echocardiogram (ECHO) OR left ventricular ejection fraction of ≥50% by ECHO or multigated acquisition scan (MUGA). 9. Normal QT interval with Fridericia correction method (QTcF) on screening electrocardiogram (ECG), defined as QTcF of ≤450 milliseconds (ms). Exclusion Criteria: 1. A history or current diagnosis of Burkitt leukemia/lymphoma or mature B-cell leukemia. 2. A history or current diagnosis of chronic myeloid leukemia (CML). 3. Diagnosis of ALL, MPAL, or Ph-like ALL with targetable kinase-activating lesions after treatment with cytotoxic therapy for another cancer. 4. Diagnosis of another concurrent primary malignancy. 5. Clinically significant cardiovascular disease, including but not limited to: 1. Any history of myocardial infarction (MI) or unstable angina. 2. History of or presence of heart block, and/or clinically significant ventricular or atrial arrhythmias. 3. Uncontrolled hypertension, defined as persistent elevation of systolic and/or diastolic blood pressures to ≥95th percentile based on age, sex, and height percentiles despite appropriate antihypertensive management. 6. Current systemic use of drug(s) that are known to have a risk of causing prolonged corrected QT interval (QTc) or torsades de pointes unless drug(s) can be changed to acceptable alternatives (ie, an alternate class of agents that do not affect the cardiac conduction system) or the participants can safely discontinue the drug(s). 7. Uncontrolled hypertriglyceridemia (triglycerides ≥450 milligrams per deciliter (mg/dL)). 8. Current systemic use of any medications or herbal supplements that are known to be strong inhibitors or strong inducers of cytochrome P450 3A (CYP3A) within 7 days before the first dose of study drug. 9. Previous treatment with ponatinib. 10. Planned non-protocol chemotherapy, radiation therapy, another investigational agent, or immunotherapy while participant is on study treatment. 11. Known gastrointestinal disease or gastrointestinal procedure that could interfere with the oral absorption of ponatinib. 12. Participants with deoxyribonucleic acid (DNA) fragility syndromes, such as Fanconi anemia and Bloom syndrome. 13. Participants with Down syndrome. 14. Participants with uncontrolled systemic infection, or known laboratory and/or clinical evidence of active infection with human immunodeficiency virus (HIV), hepatitis B, or hepatitis C. 15. Participants with pre-existing significant CNS pathology, including history of severe brain injury, dementia, cerebellar disease, organic brain syndrome, psychosis, coordination/movement disorder, or autoimmune disease with CNS involvement, are not eligible. 16. Participants with a history of cerebrovascular ischemia/hemorrhage with residual deficits are not eligible. (Participants with a history of cerebrovascular ischemia/hemorrhage remain eligible provided all neurologic deficits and causative factor(s) have resolved). 17. Uncontrolled seizure disorder. (Participants with seizure disorders that do not require antiepileptic drugs or are well controlled with stable doses of antiepileptic drugs are eligible). 18. History of severe coagulopathy or cardiovascular or peripheral vascular events. 19. Treatment with live attenuated vaccinations within 30 days prior to initiation of study treatment regimen.