Blinatumomab, Methotrexate, Cytarabine, and Ponatinib in Treating Patients With Philadelphia Chromosome-Positive, or BCR-ABL Positive, or Relapsed/Refractory, Acute Lymphoblastic Leukemia

Inclusion Criteria: 1. Diagnosis of one of the following: 1. Participants ≥ 18 years of age with previously untreated Ph-positive ALL \[either t(9;22) and/or BCR-ABL positive\] (includes patients initiated on first course of therapy before cytogenetics known) or with lymphoid accelerated or blast phase CML. These participants could have received one or two courses of chemotherapy with or without other TKIs and still eligible. (Participants with lymphoid accelerated or blast phase CML will be evaluated separately) i. If they achieved CR, they are assessable only for event-free and overall survival, or ii. If they failed to achieve CR, they are assessable for CR, event-free, and overall survival 2. Participants ≥ 18 years of age with relapsed/refractory Ph-positive ALL or with previously treated lymphoid accelerated or blast phase CML (Participants with lymphoid accelerated or blast phase CML will be evaluated separately) 3. Participants ≥ 18 years of age with ALL MRD positive (either by NGS or PCR or flowcytometry) or with previously treated lymphoid accelerated or blast phase CML (Participants with lymphoid accelerated or blast phase CML will be evaluated separately) 2. Performance status ≤ 2 (ECOG Scale) 3. Adequate liver function as defined by the following criteria (unless the increased values are judged to be leukemia disease related): 1. Total serum bilirubin ≤ 2 x upper limit of normal (ULN), unless due to Gilbert's syndrome 2. Alanine aminotransferase (ALT) ≤ 3 x ULN, OR 3. Aspartate aminotransferase (AST) ≤ 3 x ULN 4. Adequate pancreatic function as defined by the following criteria: a) Serum lipase and amylase ≤ 1.5 x ULN 5. For females of childbearing potential, a negative urine pregnancy test must be documented 6. Female participants who: * Are postmenopausal for at least 1 year before the screening visit, OR * Are surgically sterile, OR * If they are of childbearing potential, agree to practice 2 effective methods of contraception, at the same time, from the time of signing the informed consent through 4 months after the last dose of study drug, or agree to completely abstain from heterosexual intercourse 7. Male patients, even if surgically sterilized (i.e., status post-vasectomy), who: * Agree to practice effective barrier contraception during the entire study treatment period and through 4 months after the last dose of study drug, or * Agree to completely abstain from heterosexual intercourse 8. Adequate cardiac function as assessed clinically by history and physical examination. 9. Signed informed consent Exclusion Criteria: 1. Active serious infection not controlled by oral or intravenous antibiotics. 2. History of acute pancreatitis within 1 year of study or history of chronic pancreatitis 3. History of alcohol abuse 4. Uncontrolled hypertriglyceridemia (triglycerides \> 650mg/L) 5. Active secondary malignancy other than skin cancer (e.g., basal cell carcinoma or squamous cell carcinoma) that in the investigator's opinion will shorten survival to less than 1 year. 6. Active Grade III-V cardiac failure as defined by the New York Heart Association Criteria. 7. Uncontrolled, or active cardiovascular disease, specifically including, but not restricted to: * Myocardial infarction (MI), stroke, or revascularization within 3 months * Unstable angina or transient ischemic attack * Congestive heart failure prior to enrollment, or left ventricular ejection fraction (LVEF) less than lower limit of normal per local institutional standards prior to enrollment * Diagnosed or suspected congenital long QT syndrome * Clinically significant atrial or ventricular arrhythmias (such as artrial fibrillation, ventricular tachycardia, ventricular fibrillation, or Torsades de pointes) as determined by the treating physician * Prolonged QTc interval on pre-entry electrocardiogram (\> 470 msec) unless corrected after electrolyte replacement or approved by cardiologist * Significant venous or arterial thromboembolism including deep venous thrombosis or pulmonary embolism. Participants with a history of treated prior superficial or catheter associated will not be considered as significant embolism and after discussion with PI will not be excluded from eligibility. * Uncontrolled hypertension (diastolic blood pressure \>90mmHg; systolic \>140mmHg). Participants with hypertension should be under treatment on study entry to effect blood pressure control 8. History or presence of clinically relevant CNS pathology or event such as epilepsy, childhood or adult seizure, paresis, aphasia, stroke, severe brain injuries, dementia, Parkinson's disease, cerebellar disease, organic brain syndrome, psychosis or severe (grade 3 or above) CNS events including ICANS from prior CART or other T cell engager therapies. Participants with active CNS leukemia - will NOT be excluded 9. Current autoimmune disease or history of autoimmune disease with potential CNS involvement 10. Treatment with any investigational antileukemic agents or chemotherapy agents within 2 weeks prior to study entry, unless full recovery from side effects has occurred or participant has rapidly progressive disease judged to be life-threatening by the investigator. 11. Pregnant and lactating women will not be eligible; women of childbearing potential should have a negative pregnancy test prior to entering on the study and be willing to practice methods of contraception. Women do not have childbearing potential if they have had a hysterectomy or are postmenopausal without menses for 12 months. In addition, men enrolled on this study should understand the risks to any sexual partner of childbearing potential and should practice an effective method of birth control. 12. History of significant bleeding disorder unrelated to cancer, including: * Diagnosed congenital bleeding disorders (e.g., von Willebrand's disease) * Diagnosed acquired bleeding disorder within one year (e.g., acquired anti-factor VIII antibodies) 13. Participants with documented significant pleural or pericardial effusions unless they are thought to be secondary to their leukemia. 14. Known active infection with HIV, HBV, HCV.