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.