DS-1594b With or Without Azacitidine, Venetoclax, or Mini-HCVD for the Treatment of Relapsed or Refractory Acute Myeloid Leukemia or Acute Lymphoblastic Leukemia

Inclusion Criteria:

* Provision of written (signed) informed consent form (ICF) by the subject or legal guardian prior to the performance of any study-specific procedures, according to International Council on Harmonisation (ICH) and local regulatory requirements. Subject must be fully informed about their illness and the investigational nature of the study protocol (including foreseeable risks and possible toxicities) and must sign and date an Institutional Review Board (IRB)/Independent Ethics Committee (IEC) approved informed consent form (ICF)(including Health Insurance Portability and Accountability Act authorization \[HIPAA\], if applicable) before performance of any study-specific procedures or examinations
* Subjects must be willing and able to comply with the protocol
* Subjects with AML or ALL, diagnosed according to the 2016 criteria by the World Health Organization (WHO) who are refractory or relapsed (any salvage) with no available therapies or not candidates for available therapies. For subjects with prior MDS or chronic myelomonocytic leukemia (CMML) or MPN who transformed to AML, therapy received for MDS, CMML, or MPN is NOT considered as prior therapy for AML except for MDS or CMML treated with HMAs. Subjects with MDS or CMML treated with HMA therapies who progress to AML and have no available therapies or are not candidates for available therapies, will be eligible at the time of progression to AML. In Phase 1: all R/R AML or R/R ALL subjects irrespective of mutations will be eligible. In Phase 2 Cohort A only R/R AML with MLLr will be eligible. In Phase 2 Cohort B only R/R AML with NPM1m will be eligible. In Phase 2 Cohorts C and D: Only R/R AML or R/R ALL subjects with an MLLr or NPM1m will be eligible
* Prior therapy with hydroxyurea, chemotherapy, biological or targeted therapy (e.g. FLT3 inhibitors, other kinase inhibitors), or hematopoietic growth factors is permitted
* Age 18 years or older
* Eastern Cooperative Oncology Group (ECOG) performance status 0, 1, or 2
* Total bilirubin =\< 1.5 times upper limit of normal (x ULN)
* Aspartate aminotransferase or alanine aminotransferase =\< 2.5 x ULN (aspartate aminotransferase or alanine aminotransferase =\< 5.0 x ULN if deemed related to leukemia by the treating physician)
* Creatinine clearance \>= 50 mL/min as calculated using the modified Cockcroft-Gault equation
* Serum electrolytes within the institution's normal limits: potassium, calcium (total calcium, calcium corrected for serum albumin in case of hypoalbuminemia or ionized calcium) and magnesium. If outside of the institution's normal range, subject will be eligible when electrolytes are corrected
* In the absence of rapidly progressive disease, the interval from prior treatment to the time of initiation of protocol therapy will be at least 14 days for prior anti-leukemic therapy with the exception of hydroxyurea as noted below OR at least 5 half-lives for cytotoxic/noncytotoxic agents, whichever is shorter. The half-life for the therapy in question will be based on published pharmacokinetic literature (abstracts, manuscripts, investigator brochure's, or drug-administration manuals) and will be documented in the protocol eligibility document. Since the effect of therapy may be delayed, use of hydroxyurea for subjects with rapidly proliferative disease is allowed before the start of study therapy and on study and hydroxyurea will not require a washout
* Concurrent therapy for central nervous system (CNS) prophylaxis or continuation of therapy for controlled CNS disease is permitted. Subjects with a known history of CNS disease or leukemic brain metastasis must have been treated locally, have at least 3 consecutive lumbar punctures (LPs) with no evidence of CNS leukemia, and must be clinically stable for at least 4 weeks prior to enrollment and have no ongoing neurological symptoms that in the opinion of the treating physician are related to the CNS disease (sequelae that are a consequence of the treatment of the CNS disease are acceptable)
* Females must be surgically or biologically sterile or postmenopausal (amenorrheic for at least 12 months) or if of childbearing potential, must have a negative serum or urine pregnancy test within 72 hours before the start of the treatment
* Women of childbearing potential must agree to use an adequate method of contraception during the study and until 4 months after the last treatment. Males must be surgically or biologically sterile or agree to use an adequate method of contraception during the study until 3 months after the last treatment. Adequate methods of contraception include:

  * Total abstinence when this is in line with the preferred and usual lifestyle of the subject. Periodic abstinence (e.g., calendar, ovulation, symptothermal, postovulation methods) and withdrawal are not acceptable methods of contraception.
  * Female sterilization (have had surgical bilateral oophorectomy with or without 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). For female subjects on the study, the vasectomized male partner should be the sole partner for that subject
  * Combination of any of the two following (a+b or a+c or b+c)

    * a. Use of oral, injected or implanted hormonal methods of contraception or other forms of hormonal contraception that have comparable efficacy (failure rate \<1%), for example hormone vaginal ring or transdermal hormone contraception.
    * b. Placement of an intrauterine device (IUD) or intrauterine system (IUS).
    * c. Barrier methods of contraception: Condom or Occlusive cap (diaphragm or cervical/vault caps) with spermicidal foam/gel/film/cream/vaginal suppository.
  * In case of use of oral contraception, women should have been stable on the same pill before taking study treatment.
  * Note: Oral contraceptives are allowed but should be used in conjunction with a barrier method of contraception due to unknown effect of drug-drug interaction. Women are considered post-menopausal and not of child-bearing potential if they have had 12 months of natural (spontaneous) amenorrhea with an appropriate clinical profile (e.g. age appropriate, history of vasomotor symptoms) or have had surgical bilateral oophorectomy (with or without hysterectomy) or tubal ligation at least six weeks ago. In the case of oophorectomy alone, only when the reproductive status of the woman has been confirmed by follow up hormone level assessment is she considered not of child-bearing potential

Exclusion Criteria:

* Subjects with a known allergy, hypersensitivity, or contraindication to the protocol therapies or any of their components to be used in the arm the subject is to be enrolled on
* Uncontrolled or significant cardiovascular disease, including any of the following:

  * Bradycardia of less than 50 beats per minute, unless the subject has a pacemaker;
  * Corrected QT interval Fridericia's Correction Formula (QTcF) interval \> 450 msec;
  * Diagnosis of or suspicion of long QT syndrome (including family history of long QT syndrome);
  * Systolic blood pressure \>=180 mmHg or diastolic blood pressure \>=110 mmHg;
  * History of clinically relevant ventricular arrhythmias within 6 months prior to screening (eg, ventricular tachycardia, ventricular fibrillation, or Torsade de Pointes);
  * History of second (Mobitz II) or third-degree heart block (subjects with pacemakers are eligible if they have no history of fainting or clinically relevant arrhythmias while using the pacemaker);
  * History of uncontrolled angina pectoris, unstable angina or myocardial infarction, coronary artery bypass graft (CABG), cerebrovascular accident (CVA), transient ischemia attack (TIA), symptomatic pulmonary emboli within 6 months prior to screening;
  * New York Heart Association Class 3 or 4 heart failure;
  * Left ventricular ejection fraction (LVEF) =\< 50 or less than the institutional lower limit of normal;
  * Complete left bundle branch block (right bundle branch block is permitted, but requires manual reading of the QTc interval);
  * Active cardiac dysrhythmias of National Cancer Institute (NCI) Common Terminology Criteria for Adverse Events (CTCAE) grade \>= 2 (eg, atrial fibrillation)
* Persisting toxicity related to prior therapy of grade \> 1 NCI-CTCAE v 5.0; however, alopecia and sensory neuropathy grade 2 or lower is acceptable
* Underwent HSCT within 90 days of the first dose of protocol therapy, or subjects with clinically significant (grade 2 or greater) graft-versus-host disease (GVHD) (the use of topical steroids for ongoing cutaneous GVHD is permitted)
* Subjects with symptomatic CNS leukemia or subjects with poorly controlled CNS leukemia
* Active and uncontrolled disease (active infection requiring systemic therapy, fever likely secondary to infection within prior 48 hours, uncontrolled hypertension despite adequate medical therapy as judged by the treating physician)
* Active (uncontrolled, metastatic) other malignancies
* Major surgery within 28 days prior to the first dose of protocol therapy
* Known dysphagia, short-gut syndrome, gastroparesis, or other conditions that limit the ingestion or gastrointestinal absorption of drugs administered orally
* Known history of testing positive for human immunodeficiency virus (HIV) or known acquired immunodeficiency syndrome (test at screening only if required by local regulations)
* Known history of hepatitis B virus (HBV) or hepatitis C virus (HCV) infection with active Hepatitis B or C infection at screening (positive HBV surface antigen or HCV ribonucleic acid \[RNA\] if anti-HCV antibody screening test positive)
* Vaccination within 4 weeks of the first dose of study drug and while on trials is prohibited except for administration of inactivated vaccines
* Subjects who are currently receiving treatment with medication that meet one of the following criteria and that cannot be discontinued at least one week prior to the start of DS-1594b treatment:

  * Medications that may prolong QTc interval and have a known risk of inducing Torsades de Pointes unless it is vital for the care of the subjects
  * Strong inhibitors or inducers of CYP3A
  * CYP3A and CYP2C19 substrates with narrow therapeutic index
* Subjects who consume grapefruit products, Seville oranges, or star fruit within 3 days prior to the first DS-1594b administration and until the last day of DS-1594b is completed
* SUB-STUDIES: Subjects who are currently receiving moderate inhibitors or inducers of CYP3A who cannot discontinue at least one week prior to the start of DS-1594b treatment till the end of sub-study period
* SUB-STUDIES: Subjects who are currently receiving proton pump inhibitors who cannot discontinue at least 2 days prior to the start of DS-1594b treatment till the end of sub-study period
* Other severe acute or chronic medical conditions that is active and not well controlled including renal, skeletal muscle, adrenal insufficiency, colitis, inflammatory bowel disease, or psychiatric conditions including recent (within the past year) or active suicidal ideation or behavior; or laboratory abnormalities that may increase the risk associated with study participation or study treatment administration or may interfere with the interpretation of study results and, in the judgment of the investigator, would make the subject inappropriate for entry into this study
* Subjects unwilling or unable to comply with the protocol, including:

  * Pregnant or breastfeeding women or women of childbearing potential who are unable to comply with appropriate contraception as outlined in or who plan to become pregnant while in the study or for at least 6-7 months after last administration of study treatment
  * Known alcohol or drug abuse within the last 1 year
  * In a man whose sexual partner is a woman of childbearing potential, unwillingness or inability to use an acceptable contraceptive method for the entire study period and for at least 3 months after study completion
* Acute promyelocytic leukemia (APL)
* Uncontrolled or poorly controlled adrenal or pituitary disease (including adrenal insufficiency, Addison's disease, Cushing's disease)