Safety and Efficacy of Ponatinib for Treatment of Pediatric Recurrent or Refractory Leukemias, Lymphomas or Solid Tumors

Inclusion Criteria: Histologically or cytologically confirmed diagnosis of the following malignancies: \- Phase 1: CP-CML, BP-CML, AP-CML ALL. AML. Other leukemias. Lymphoma. Any other tumors, including tumors of the CNS, for which standard therapy is not available or is not indicated. \- Phase 2, Group A with CP-CML: CP-CML at the time of study entry and must be resistant to or intolerant of at least 1 prior BCR-ABL-targeted TKI therapy or be in "warning" response status or have the T315I kinase domain mutation. Must have 1 bone marrow aspirate with documentation of BCR-ABL translocation by conventional cytogenetics, metaphase FISH, or q-PCR performed within 42 days before the first dose of ponatinib. \- Phase 2, Group B with other leukemias or solid tumors: ALL. AML. Other leukemias. Lymphoma. Any other tumors, including tumors of the CNS, with mutations of RET, FLT3, KIT, FGFR, PDGFR, TIE2, VEGFR, or any other mutations where ponatinib may have biological activity (eg, EPH receptors and SRC families of kinases) as assessed on fresh or archived tumor tissue. Participants with solid tumors or with lymphoma must have measurable disease by CT or MRI based on RECIST v1.1 or the Lugano lymphoma guidelines as determined by site radiology. Prior therapies as follows: \- Phase 1: Participants with CML who are resistant to or intolerant of (as defined Appendix F) to at least 1 prior BCR-ABL-targeted TKI therapy. Participants with ALL who have progressed on or after all available or indicated therapies, which may have included 1 prior BCR-ABL-targeted TKI therapy. Participants with AML or other leukemias who have progressed on or after at least 1 prior induction attempt (for France only) or for whom no effective standard therapy is available or indicated (other countries). Participants with solid tumors (including tumors of the CNS) or lymphomas who have progressed despite standard therapy or for whom no effective standard therapy is available or indicated. \- Phase 2, Group A with CP-CML: Participants who are resistant to or intolerant of at least 1 prior BCR-ABL-targeted TKI therapy. \- Phase 2, Group B with other leukemias or solid tumors: Participants with ALL who have progressed on or after all available or indicated therapies, which must have included 1 prior BCR-ABL-targeted TKI therapy. Participants with AML or other leukemias who have progressed on or after at least 1 prior induction attempt (for France only) or for whom no effective standard therapy is available or indicated (other countries). Participants with solid tumors (including tumors of the CNS) or lymphomas who progressed despite standard therapy or for whom no effective standard therapy is available or indicated. * Karnofsky performance status ≥ 40% for participants ≥ 16 years old or Lansky Play Scale ≥ 40% for pediatric participants \< 16 years old. * Participants must have recovered to \< Grade 2 per the NCI CTCAE v5.0 or to baseline from any non-hematologic toxicities (except alopecia) due to previous therapy. * Willingness to avoid pregnancy or fathering children. Exclusion Criteria: Prior therapies: \- Participants with BP-CML, ALL, or AML who have received any of the following: Corticosteroids or hydroxyurea within 24 hours before the first dose of ponatinib. Vincristine within 7 days before the first dose of ponatinib. Other chemotherapy (excluding intrathecal chemotherapy) within 14 days before the first dose of ponatinib. \- Participants (except the BP-CML, ALL, and AML participants described above) who: Have had cytotoxic chemotherapy within 21 days (or 42 days for nitrosoureas or mitomycin C) before the first dose of ponatinib. Prior radiation therapy or radio-isotope therapy within 6 weeks before the first dose of ponatinib except local radiotherapy for palliative indication within 14 days before the first dose of ponatinib. Autologous or allogeneic stem cell transplant \< 3 months before the first dose of ponatinib. Major surgery within 14 days before the first dose of ponatinib. Inadequate recovery and/or complications from a major surgery before starting therapy. Prior treatment with any of the following: * Immunosuppressive therapy (including post stem cell transplant regimens) within 14 days before the first dose of ponatinib. * Any targeted cancer therapy (including TKIs) within 7 days before the first dose of ponatinib. * Any other investigational anticancer agents within 30 days or 5 half-lives, whichever is longer, before randomization. * Any monoclonal antibody-directed anticancer therapy within 5 half-lives of the first dose of ponatinib. * Any chimeric antigen receptor therapy within 28 days before the first dose of ponatinib * Ponatinib * Protocol-defined lab Values * Significant concurrent, uncontrolled medical condition, including but not limited to the following: * Pancreatic: clinical, radiological, or laboratory evidence of pancreatitis. * Cardiac: * SF \< 27% by ECHO, OR EF \< 50% by MUGA. * Abnormal QTcF on screening ECG, defined as QTcF of ≥ 450 ms. * Clinically significant or uncontrolled cardiovascular disease, including unstable angina, acute MI within 6 months from Day 1 of study drug administration, New York Heart Association Class III or IV CHF (see Appendix P), and arrhythmia requiring therapy unless approved by the medical monitor/sponsor. * Uncontrolled hypertension. * Currently taking drug(s) that are known to have a risk of causing prolonged QTc or TdP unless the drug(s) can be changed to acceptable alternatives (ie, an alternate class of agents that do not affect the cardiac conduction system), or the participant can safely discontinue the drug(s). * Cerebral: * Participants with solid tumors with intracranial metastasis OR participants with active CNS leukemia (ie, CNS-2 status \[\< 5/μL WBCs and cytospin positive for blasts, or ≥ 5 /μL WBCs but negative by Steinherz/Bleyer algorithm (equation used for traumatic lumbar punctures), disseminated leptomening