ABL001 + Dasatinib + Prednisone + Blinatumomab in BCR-ABL+ B-ALL or CML

Inclusion Criteria: * Participants must meet the following criteria on screening examination to be eligible to participate in the study: * Participants must have cytopathologically confirmed CD19+ BCR-ABL1+ acute leukemia (B-cell ALL, mixed phenotype acute leukemia, or CML in lymphoid blast crisis with ≥ 5% lymphoblasts.)22 * BCR-ABL1 positive status may be confirmed by FISH, karyotype analysis, or molecular testing for p210 (b2a2 or b3a2) or p190 (e1a2) transcripts. * Patients with asymptomatic central nervous system (CNS) disease are eligible and may be treated concurrently with intrathecal chemotherapy. * Dose escalation: Participants must NOT be suitable for or willing to receive standard intensive induction chemotherapy. * Dose expansion: Participants aged 18 years and older will be eligible regardless of suitability for intensive induction chemotherapy. The following groups are not considered suitable for standard intensive induction chemotherapy: * Participants who have not received standard intensive induction chemotherapy and are aged ≥ 50 years. * Participants who have not received standard intensive induction chemotherapy and are aged 18 to 49 years and unfit due to co-morbidity or other factors to receive intensive chemotherapy. Specific criteria that would suggest that a patient is unsuitable for intensive induction chemotherapy include: * Severe cardiac comorbidity (congestive heart failure or documented cardiomyopathy with EF ≤50%). * Severe pulmonary comorbidity (documented pulmonary disease with DLCO ≤ 65% or FEV1 ≤ 65%, or dyspnea at rest, or requiring oxygen). * ECOG performance status of 2 due to medical conditions unrelated to leukemia. * Any other comorbidity that the physician judges to be incompatible with intensive cytotoxic chemotherapy. * Participants aged ≥ 18 years with disease that is relapsed or refractory to 1 or more cycles of standard intensive induction chemotherapy. * ECOG performance status 0-3 (Appendix A). ECOG value of 3 is allowed after documented discussion with PI, if poor performance status is attributed to underlying disease. * Participants must have normal organ function as defined below: * Creatinine ≤ 1.5x institutional upper limit of normal. * Amylase and lipase values ≤ 3.0x institutional upper limit of normal. * Alkaline phosphatase ≤ 2.5x institutional upper limit of normal (unless considered to be not of hepatic origin) (any level permitted), and/or unless felt to be clearly related to disease where ≤ 5x institutional upper limit of normal is permitted, after discussion with the overall PI. * AST(SGOT)/ALT(SGPT) ≤ 3x institutional upper limit of normal unless felt to be clearly related to disease where ≤ 5x institutional upper limit of normal is permitted, after discussion with the overall PI. * Total bilirubin - ≤1.5x institutional upper limit of normal (≤ 3x upper limit of normal in patients with known or suspected Gilbert's syndrome). The effects of ASCIMINIB on the developing human fetus are unknown. For this reason, women of child-bearing potential and men must agree to use adequate contraception (hormonal or barrier method of birth control; abstinence) prior to study entry and for the duration of study participation. * Women of child-bearing potential must agree to use highly effective methods of contraception during dosing and for 30 days after study treatment. 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. * Allowable methods of birth control: * Total abstinence (when this is in line with the preferred and usual lifestyle of the subject). Periodic abstinence (e.g., calendar, ovulation, symptothermal, post ovulation methods) and withdrawal are not acceptable methods of contraception. * Female sterilization (have had surgical bilateral oophorectomy with or without hysterectomy), total hysterectomy, or tubal ligation at least six weeks before taking study treatment. In case of oophorectomy alone, only when the reproductive status of the woman has been confirmed by follow up hormone level assessment. * Male sterilization (at least 6 months prior to screening). The vasectomized male partner should be the sole partner for that subject. * Use of oral, injected or implanted hormonal methods of contraception or placement of an intrauterine device (IUD) or intrauterine system (IUS), or other forms of hormonal contraception that have comparable efficacy (failure rate \<1%), for example hormone vaginal ring or transdermal hormone contraception. * Sexually active males must use a condom during intercourse while taking the drug and for 30 days after stopping treatment and should not father a child in this period. A condom is required to be used also by vasectomized men in order to prevent delivery of the drug via seminal fluid. -- Ability to understand and the willingness to sign a written informed consent document and comply with all study procedures. Exclusion Criteria: * For dose escalation only: Participants suitable for and willing to receive standard intensive induction chemotherapy. * Patients with a known ABL T315I mutation are excluded. ABL kinase mutation analysis is not recommended for newly diagnosed patient. ABL kinase mutation analysis is recommended for patients with relapsed disease or CML progressed to blast phase on prior TKI, and results should be reviewed prior to enrollment. * Prior treatment of ALL or CML with dasatinib or ASCIMINIB. Prior receipt of other TKIs and chemotherapy for the treatment of ALL or CML is permitted. * Any TKI therapy must be discontinued for 5 half-lives prior to initiation of protocol therapy. * Patient may not have received other chemotherapy, including antibody-based therapy, within 2 weeks of the initiation of protocol therapy with the exception of steroids, hydroxyurea, ATRA, and/or intrathecal chemotherapy. * Participants who are receiving any other investigational agents for conditions other than ALL must have discontinued those agents 2 weeks prior to the start of study treatment. * Impairment of gastrointestinal (GI) function or GI disease that may significantly alter the absorption of study drug (e.g., ulcerative disease, uncontrolled nausea, vomiting, diarrhea, malabsorption syndrome). Patients who have had a gastrectomy are not excluded. * History of prior or concurrent malignancy requiring current treatment and/or whose natural history has the potential to interfere with the safety or efficacy assessment of the investigational regimen. Indolent or low risk cancers (i.e. early stage prostate cancer, early stage breast cancer, asymptomatic meningioma) judged to not require treatment and/or have low potential for progression/recurrence after appropriate therapy may be permitted after discussion with overall PI. * Acute or chronic liver disease (including known active hepatitis B and C infections). Screening for hepatitis is not required. Patients with known treated or past exposure viral hepatitis may participate after confirmation of absence of active infection (i.e. negative viral load). * History of pulmonary arterial hypertension. * Significant pleural effusions leading to respiratory compromise and need for intervention (i.e. thoracentesis). * Alcohol abuse requiring medical treatment. * Participants with a history of or current acute pancreatitis, chronic pancreatitis, or any ongoing pancreatic disease. * Known human immunodeficiency virus (HIV). Screening is not required. * History of a serious bleeding disorder unrelated to ALL. * It is suggested that participants receiving treatment with medications that meet one of the following criteria discontinue the relevant drug prior to the start of treatment with ASCIMINIB and for the duration of the study. If the medication is medically necessary, review with PI before enrollment. * Strong inducers of CYP3A4/5. * Moderate and strong inhibitors CYP3A4/5. * CYP3A4/5, CYP2C8 and CYP2C9 substrates with narrow therapeutic index. All other substrates of the enzymes should be used with caution. * H2 antagonists/proton-pump inhibitors. * Grapefruit products are not permitted while on study. * Because the lists of these agents are constantly changing, it is important to regularly consult a frequently-updated list such as http://medicine.iupui.edu/clinpharm/ddis/table.aspx; medical reference texts such as the Physicians' Desk Reference may also provide this information. As part of the enrollment/informed consent procedures, the patient will be counseled on the risk of interactions with other agents, and what to do if new medications need to be prescribed or if the patient is considering a new over-the-counter medicine or herbal product. * Corrected QT interval (QTc) of \> 480 milliseconds (ms) on baseline electrocardiogram (ECG) (using corrected QT interval per institutional standard). * Major surgery within 2 weeks before the first dose of ASCIMINIB. * Uncontrolled intercurrent illness including, but not limited to: * Uncontrolled infection. * Unstable cardiovascular condition including symptomatic congestive heart failure (NYHA class 3 or 4), unstable angina pectoris, ongoing clinically significant cardiac arrhythmia uncontrolled by medication, and myocardial infarction or stroke within the past 3 months. * Psychiatric illness/social situations that would limit compliance with study requirements. * Currently requiring supplemental oxygen, mechanical ventilation, vasopressors, and/or hemodialysis (life-support). * History of significant congenital or acquired bleeding disorder unrelated to cancer. * Unable to comply with an oral regimen. * Are pregnant or nursing at the time of screening. Pregnant women are excluded from this study because ASCIMINIB is an agent with 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 ASCIMINIB, breastfeeding should be discontinued if the mother is treated with ASCIMINIB. These potential risks may also apply to other agents used in this study. Urine or serum pregnancy test must be performed within 14 days of Day 1 for women of childbearing potential.