A Study of TAS0728 in Patients With Solid Tumors With HER2 or HER3 Abnormalities

Inclusion Criteria: 1. Male or females with an age ≥ 18 years. 2. Subjects with histological- or cytological-confirmed, advanced cancer, who have progressed on (or not been able to tolerate) standard therapy or for whom no standard anticancer therapy exists 1. For Phase 1, only subjects HER2 or HER3 molecular/genetic alterations will be enrolled. 2. For Phase 2a, subjects with one of the following tumor types will be enrolled: i. Urothelial cancer with HER2 or HER3 mutation ii. Biliary tract cancer with HER2 or HER3 mutation iii. Breast cancer with HER2 or HER3 mutation iv. Breast cancer with HER2 amplification or overexpression v. NSCLC with HER2 or HER3 mutation vi. CRC with HER2 mutation or amplification vii. Other tumors with HER2 mutation/amplification/overexpression or HER3 mutation (gastric/GEJ, endometrial). 3. At least 1 measurable lesion for solid tumor 4. Is able to take medications orally (e.g., no feeding tube). 5. Able to agree to and sign informed consent and to comply with the protocol 6. Has adequate organ function Exclusion Criteria: 1. Has a serious illness or medical condition(s) 2. Has received treatment with any proscribed treatments within specified time frames prior to study drug administration 3. Impaired cardiac function or clinically significant cardiac disease