Study of TT-00420 (Tinengotinib) Tablet as Monotherapy and Combination Therapy in Patients With Advanced Solid Tumors

Inclusion Criteria: 1. ≥ 18 years of age 2. Histopathological or cytologically documented locally advanced or metastatic solid tumors who have no available standard therapeutic treatment options 3. At least one measurable lesion as defined by RECIST V1.1 criteria for solid tumors 4. Eastern Cooperative Oncology Group (ECOG) performance status of 0 or 1 5. Adequate organ function confirmed at screening and within 10 days of initiating treatment, as evidenced by: * Absolute neutrophil count (ANC) ≥ 1.5 x 10\^9/L * Hemoglobin (Hgb) ≥ 8 g/dl * Platelets (plt) ≥ 75 x 10\^9/L * AST/SGOT and ALT/SGPT ≤ 2.5 x Upper Limit of Normal (ULN) or ≤ 5.0 x ULN if liver metastases are present * Total bilirubin ≤ 1.5 x ULN * Calculated creatinine clearance ≥ 50 mL/min (Cockcroft Gault formula) 6. Negative pregnancy test within 72 hours before starting study treatment in all premenopausal women and women \< 12 months after the onset of menopause 7. Must agree to take sufficient contraceptive methods to avoid pregnancy during the study and until at least 6 months after ceasing study treatment 8. Able to sign informed consent and comply with the protocol Exclusion Criteria: 1. Women who are pregnant or lactating 2. Women of child-bearing potential (WOCBP) who do not use adequate birth control 3. Patients with any hematologic malignancy, including leukemia (any form), lymphoma, and multiple myeloma 4. Patients with a history of primary central nervous system tumors or carcinomatous meningitis. 5. Patients with the following mood disorders as judged by the Investigator or a psychiatrist: * Medically documented history of or active major depressive episode, bipolar disorder (I or II), obsessive-compulsive disorder, schizophrenia; a history of suicidal attempt or ideation, or homicidal ideation (immediate risk of doing harm to others) * ≥ CTCAE grade 3 anxiety 6. Impaired cardiac function or significant diseases, including but not limited to any of the following: * left ventricular ejection fraction (LVEF) \< 45% as determined by multigated acquisition (MUGA) scan or echocardiogram (ECHO) * Congenital long QT syndrome * QTcF ≥ 480 msec on screening ECG * Unstable angina pectoris ≤ 3 months prior to starting study drug * Acute myocardial infarction ≤ 3 months prior to starting study drug 7. Patients with: * unresolved diarrhea ≥ CTCAE grade 2, or * impairment of gastrointestinal (GI) function, or * GI disease that may significantly alter the absorption of TT-00420 8. Other concurrent severe and/or uncontrolled concomitant medical conditions (e.g., uncontrolled hypertension, uncontrolled hypertriglyceridemia, or active or uncontrolled infection) that could cause unacceptable safety risks or compromise compliance with the protocol 9. Patients who have received chemotherapy, targeted therapy, or immunotherapy ≤ 4 weeks (6 weeks for nitrosourea or mitomycin-C) prior to starting study drug or who have not recovered from side effects of such therapy 10. Patients who have received wide field radiotherapy ≤ 4 weeks or limited field radiation for palliation ≤ 2 weeks prior to starting study drug or who have not recovered from side effects of such therapy 11. Patients who have undergone major surgery ≤ 4 weeks prior to starting study drug or who have not recovered from side effects of such therapy 12. Patients who have been treated with any hematopoietic colony-stimulating growth factors (e.g., G-CSF, GM-CSF) ≤ 4 weeks prior to starting study drug. 13. Patients who are currently receiving treatment with therapeutic doses of warfarin sodium or any other coumarin-derivative anticoagulants 14. Patients who have received systemic corticosteroids ≤ 2 weeks prior to starting study drug or who have not recovered from the side effects of such treatment. 15. Patients who are currently receiving treatment with strong CYP3A inhibitors or inducers ≤ 2 weeks prior to starting study drug. 16. Known diagnosis of human immunodeficiency virus (HIV) infection (HIV testing is not mandatory; patients with well controlled HIV might be enrolled) 17. Known history of active infection with Hepatitis B or Hepatitis C 18. Has received a live-virus vaccination within 30 days of planned first dose 19. Inability to swallow or tolerate oral medication 20. Has a history or current evidence of any condition, therapy, or laboratory abnormality that, in the opinion of the investigator, might confound the results of the trial, interfere with the patient's safe participation and compliance in the trial.