A Study of TAS1553 in Subjects With Relapsed or Refractory Acute Myeloid Leukemia (AML) and Other Myeloid Neoplasms

Inclusion Criteria: 1. Capable of giving signed informed consent. 2. Participant must be 18 years of age or older, at the time of signing the informed consent. 3. Life expectancy of at least 12 weeks as assessed by the investigator. 4. Participants with R/R AML or other myeloid neoplasms where approved therapies have failed or for whom known life-prolonging therapies are not available. The AML population includes de novo AML, secondary AML, and MDS transformed into AML. Other myeloid neoplasms include accelerated phase MPN, and chronic or accelerated phase MPN-U and MDS-MPN. Blast crisis phase of MPN, MPN-U, and MDS-MPN are considered secondary AML and will be included in the AML cohort. 5. Have an Eastern Cooperative Oncology Group (ECOG) performance status of 0 to 1. 6. Have platelet count ≥10,000/μL (transfusions to achieve this level are allowed). 7. Have adequate renal function as demonstrated by a 24-hour urine measured creatinine clearance ≥60 mL/min. 8. Adequate hepatic function as evidenced by: 1. aspartate aminotransferase (AST) ≤3× upper limit of normal (ULN) 2. alanine aminotransferase (ALT) ≤3×ULN 3. total bilirubin ≤1.5×ULN. 9. Participants must be amenable to serial bone marrow biopsies, peripheral blood sampling, and urine sampling during the study. 10. Women of child-bearing potential (according to recommendations of the Clinical Trial Facilitation Group \[CTFG\]) must not be pregnant or breastfeeding and must have a negative pregnancy test at screening. Exclusion Criteria: 1. Participants who have MPN, MPN-U, or MDS/MPN and display hypoplastic bone marrow and would also not ordinarily benefit from cytoreductive therapy such as hydroxyurea (HU). 2. Participants with highly proliferative disease are excluded as follows: 1. Part 1/AML: white blood cells (WBC) \>20,000/μL and \>50% blasts in blood. Measures to reduce WBC, such as HU treatment within the last 2 weeks and cytotoxic chemotherapy within the last 4 weeks are not allowed to meet this eligibility criterion. 2. Part 1/other myeloid neoplasms: WBC \>20,000/μL. A short course of HU may be used to meet this eligibility criterion, as long as HU is discontinued 96 hours and any encountered drug-related toxicity must be resolved to Grade ≤1 before the first dose of study treatment. 3. Part 2/Cohort 1, AML: WBC\>20,000/μL and \>50% blasts in blood. A short course of HU may be used to meet this eligibility criterion, as long as HU is discontinued 96 hours, and any encountered drug-related toxicity must be resolved to Grade ≤1 before the first dose of study treatment. 4. Part 2/Cohort 2, other myeloid neoplasms: Specific WBC exclusion criterion not defined. A short course of HU may be used to reduce WBC if judged to be necessary by the investigator, as long as HU is discontinued 96 hours and any encountered drug-related toxicity must be resolved to Grade ≤1 before the first dose of study treatment. 3. Known clinically active central nervous system (CNS) leukemia. 4. Diagnosis of BCR-ABL-positive leukemia, acute promyelocytic leukemia (M3 AML or APML), or juvenile myelomonocytic leukemia (JMML). 5. Second malignancy requiring active systemic therapy, except breast or prostate cancer stable on or responding to endocrine therapy. 6. Ongoing Grade ≥3 Graft Versus Host Disease (GVHD), or any grade GVHD requiring active treatment (for example, calcineurin inhibitors, ≥5mg/day prednisone or other steroid equivalent, or other immunosuppressive agents). (Note: Prednisone at any dose for other indications is allowed). 7. Advanced human immunodeficiency virus (HIV) infection, active hepatitis B virus (HBV) or hepatitis C virus (HCV) infection; Inactive hepatitis carrier status and participants with laboratory evidence of no active replication and participants on antiviral medication(s) who have a viral load below limit of detection will be permitted. 8. Known significant mental illness or other condition such as active alcohol or other substance abuse or addiction that, in the opinion of the investigator, predisposes the participant to high risk of non-compliance with the protocol. 9. Active infection resistant to antibiotics; or non-leukemia-associated pulmonary disease requiring \>2 liters per minute oxygen or any other condition that puts the participant at an imminent risk of death. 10. 24-hour urinary protein excretion ≥1g or urinalysis of 2+proteinuria. 11. History of, or at risk for, cardiac disease, as evidenced by any of the following conditions: 1. Abnormal left ventricular ejection fraction (LVEF; \<50%) on echocardiogram (ECHO) or multiple-gated acquisition (MUGA) scan at Screening. 2. Congestive cardiac failure of Class ≥III severity according to New York Heart Association (NYHA) functional classification defined as patients with marked limitation of activity and who are comfortable at rest, while Class IV patients have symptoms of heart failure at rest. 3. Unstable cardiac disease including unstable angina or hypertension as defined by the need for overnight hospital admission within the last 3 months (90 days). 4. Ventricular arrhythmias including ventricular bigeminy, clinically significant brady arrhythmias such as sick sinus syndrome, third-degree atrioventricular (AV) block, presence of cardiac pacemaker or defibrillator, or other clinically significant arrhythmias. 5. Screening 12-lead electrocardiogram (ECG) with measurable QTcF interval of ≥470 msec (Fridericia's formula should be used). 12. Known hypersensitivity to TAS1553 or any of its components. 13. Allogenic hematopoietic stem cell transplantation (HSCT) within 180 days of the first dose of TAS1553, or participants on immunosuppressive therapy post HSCT at the time of screening (calcineurin inhibitors or similar must be discontinued ≥4 weeks prior to the time of study drug initiation). 14. Treated with any systemic anticancer therapy within 2 weeks of the first dose of study treatment. Any encountered treatment-related toxicities (excepting alopecia) must be resolved to Grade 1 or less. 15. Phase 1 Part 1 only: participants who require concomitant use of strong CYP3A4 inducers. 16. Inability to swallow oral medication.