A Study of TAS1440 With ATRA in Subjects With r/r AML

Inclusion Criteria: 1. Have a projected life expectancy of at least 12 weeks and be in stable condition to complete 1 full cycle (4 weeks) of treatment. 2. Have histological confirmation of AML by World Health Organization (WHO) 2016 criteria and who have failed all other available conventional therapies. 3. Have a peripheral blood or bone marrow blast count \>5% at the time of enrollment. 4. Have disease that: 1. is refractory to standard induction chemotherapy, including but not limited to anthracycline and cytarabine combination therapy, or 2. has relapsed after anthracycline and cytarabine therapy or stem cell transplant (SCT), or 3. is refractory to or has relapsed after a front-line regimen containing a hypomethylating agent, alone or in combination. 5. Have an Eastern Cooperative Oncology Group (ECOG) Performance status of 0 to 1. 6. Have adequate renal function as demonstrated by a serum creatinine ≤1.5 × upper limit of normal (ULN) or calculated creatinine clearance (by the standard Cockcroft-Gault formula) of ≥60 mL/min. 7. Have adequate liver function as demonstrated by the following: 1. aspartate aminotransferase (AST) and alanine aminotransferase (ALT) \<3 × upper limit of normal (ULN) 2. AST and ALT \<5 × ULN (if considered due to leukemic organ involvement). 8. 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. Known clinically active central nervous system leukemia. 2. BCR-ABL-positive leukemia. 3. Diagnosis of acute promyelocytic leukemia (M3 AML or APML or APL). 4. Second malignancy currently requiring active therapy, except breast or prostate cancer stable on or responding to endocrine therapy. 5. Grade 3 or higher graft versus host disease (GVHD), or GVHD requiring treatment with either: 1. a calcineurin inhibitor, or 2. prednisone more than 5 mg/day (Note: Prednisone at any dose for other indications is allowed). 6. Total serum bilirubin ≥1.5 × ULN (except for subjects with Gilbert's Syndrome for whom direct bilirubin is \>2.5 × ULN), or liver cirrhosis, or chronic liver disease Child-Pugh Class B or C. 7. Known active human immunodeficiency virus (HIV), hepatitis B virus (HBV), or hepatitis C virus (HCV) infection. Inactive hepatitis carrier status or low viral hepatitis titer being treated with antivirals is allowed. For subjects considered at risk of viral exposure, serologies should be used to establish negativity. 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 subject to high risk of non-compliance with the protocol. 9. Myocardial impairment of any cause (eg, cardiomyopathy, ischemic heart disease, significant valvular dysfunction, hypertensive heart disease, or congestive heart failure) resulting in heart failure by New York Heart Association (NYHA) Criteria (Class III or IV staging). 10. Screening 12-lead echocardiogram with measurable QTc interval (according to either Fridericia's or Bazett's correction) of \>480 milliseconds. 11. Active, uncontrolled infection. Participants with an infection receiving treatment (antibiotic, antifungal, or antiviral treatment) must be afebrile and hemodynamically stable for ≥72 hours before enrollment. 12. Non-AML-associated pulmonary disease requiring \>2 liters per minute (LPM) oxygen. 13. Proliferative AML with total white blood cells \> 20,000/uL 14. Any other condition that puts the participant at an imminent risk of death. 15. Treated with any investigational therapy within 2 weeks of the first dose of study treatment. 16. Inability to swallow oral medication. 17. Known hypersensitivity to ATRA, any of its components, or other retinoids. 18. Known sensitivity to parabens.