Inclusion Criteria:
* Age 18 to 70 years. Because no dosing or adverse event data are currently available on the use of the combination of FLAG-Ida with venetoclax and asciminib in patients \<18 years of age, children are excluded from this study.
* Newly diagnosed or relapsed/refractory:
* BCR::ABL1-rearranged CML in myeloid BP or Philadelphia chromosomepositive or BCR::ABL1-rearranged AML as defined by the WHO 2022 criteria23
* BCR::ABL1-rearranged CML in lymphoid BP.
* ECOG performance status ≤ 2.
* Adequate liver, cardiac, renal and pancreatic function as defined by the following criteria:
* Total serum bilirubin ≤ 1.5 x upper limit of normal (ULN), unless due to Gilbert's syndrome, hemolysis, or the underlying leukemia approved by the Principal Investigator (PI)
* Alanine aminotransferase (ALT) or aspartate aminotransferase (AST) ≤ 3 x ULN, unless due to the underlying leukemia approved by the PI
* Creatinine clearance ≥ 30 mL/min
* Serum amylase or lipase ≤ 1.5 x ULN
* Left ventricular ejection fraction ≥ 40%.
* 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.
* Human immunodeficiency virus (HIV)-infected patients on effective anti-retroviral therapy with undetectable viral load within 6 months are eligible for this trial.
* Patients with a prior or concurrent malignancy whose natural history or treatment does not interfere with the safety or efficacy assessment of the investigational regimen are eligible for this trial.
* Because the therapeutic agents used in this trial could potentially be teratogenic, women of childbearing potential and men must agree to use adequate contraception prior to study entry and for the duration of study participation. This includes all female patients, up until the age of 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 4 months after completion of trial treatment
* Ability to understand and the willingness to sign a written informed consent document.
Exclusion Criteria:
* Patients who are receiving any other investigational agents used for the treatment of other cancers.
* Patients who have progressed on asciminib and/or a combination of intensive chemotherapy plus venetoclax. Patients with prior treatment with a hypomethylating agent and venetoclax will be eligible.
* Active grade III-V cardiac failure as defined by the New York Heart Association Criteria.
* Myocardial infarction, unstable angina, or stroke within 3 months prior to signing informed consent.
* Clinically significant atrial or ventricular arrhythmias (such as uncontrolled, clinically significant atrial fibrillation, ventricular tachycardia, ventricular fibrillation, or Torsades de pointes) as determined by the treating physician.
* Prolonged QTcF interval on pre-entry electrocardiogram (\> 470 msec) unless corrected after electrolyte replacement or approved by a cardiologist.
* History of acute pancreatitis within 6 months or medical history of chronic pancreatitis.
* Active serious infection not controlled by oral or intravenous antibiotics (e.g. persistent fever or lack of improvement despite antimicrobial treatment).
* Active secondary malignancy that in the investigator's opinion will shorten survival to less than one year.
* Treatment with any investigational antileukemic agent in the last 14 days before study entry, unless full recovery from side effects has occurred or patient has rapidly progressive disease judged to be life-threatening by the investigator. Prior recent treatment with corticosteroids, hydroxyurea, cytarabine (up to 2 g/m2 given for cytoreduction within the preceding 7 days) and/or an FDA-approved BCR::ABL1 TKI is permitted.
* History of allergic reactions attributed to compounds of similar chemical or biologic composition to the combination of FLAG-Ida, venetoclax, asciminib, or blinatumomab.
* Pregnant women are excluded from this study because study drugs have the potential for teratogenic or abortifacient effects. Because there is an unknown but potential risk for adverse events in nursing infants secondary to treatment of the mother with study drugs, breastfeeding should be discontinued.
* Patients with psychiatric illness/social situations that would limit compliance with study requirements.
