Safety of TT-00420 (Tinengotinib) Monotherapy in Patients With Advanced Solid Tumors and Triple Negative Breast Cancer

Inclusion Criteria: 1. Aged 18 years to 75 years at the time of provision of informed consent 2. Dose Escalation Cohorts: Histopathological or cytologically documented locally advanced or metastatic solid tumors who have no available standard therapeutic treatment options Dose Expansion Cohorts: Histopathological or cytologically documented locally advanced or metastatic TNBC or SATs 3. TNBC Dose Expansion Cohort: 1. Histologically proven invasive breast carcinoma with triple negative receptor status per institutional standard and with confirmed negative for ER and PR by IHC (\<10% positive tumor nuclei) 2. relapsed/refractory to at least one line of systemic chemotherapy 4. At least one measurable lesion as defined by RECIST V1.1 criteria for solid tumors 5. ECOG performance status of 0 or 1 6. 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) ≥ 9 g/dl * Platelets (plt) ≥ 100 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, or direct bilirubin \< ULN for patients with total bilirubin levels \>1.5 ULN * Serum creatinine ≤ 1.5 x ULN or calculated 24-hour clearance ≥ 50 mL/min * Negative pregnancy test within 72 hours before starting study treatment in all pre-menopausal 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 to comply with the protocol Exclusion Criteria: 1. Women who are pregnant or lactating 2. Women of child-bearing potential (WOCBP) who does not use adequate birth control 3. Patients with any hematologic malignancy. This includes leukemia (any form), lymphoma, and multiple myeloma. 4. Patients with 1. a history of primary central nervous system tumors or 2. carcinomatous meningitis Note: Patients with treated brain metastases that are off corticosteroid and have been clinically stable 28 days are eligible for enrollment 5. Patients with the following mood disorders as judged by the Investigator or a psychiatrist, or as result of patient's mood assessment questionnaire: * 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 * The psychiatric judgment, if available, overrules the mood assessment questionnaire result/investigator judgment 6. Impaired cardiac function or clinically significant cardiac diseases, including but not limited to any of the following: 1. LVEF \< 45% as determined by MUGA scan or ECHO 2. Congenital long QT syndrome 3. QTc ≥ 450 msec on screening ECG 4. Unstable angina pectoris ≤ 3 months prior to starting study drug 5. Acute myocardial infarction ≤ 3 months prior to starting study drug 7. Patients with 1. unresolved diarrhea ≥ CTCAE grade 2, or 2. impairment of gastrointestinal (GI) function, or 3. GI disease that may significantly alter the absorption of TT-00420 (e.g., ulcerative diseases, uncontrolled nausea, vomiting, diarrhea, malabsorption syndrome, or small bowel resection). 8. Other concurrent severe and/or uncontrolled concomitant medical conditions (e.g., uncontrolled hypertriglyceridemia \[triglycerides \> 500 mg/dL\], 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) ≤ 2 weeks prior to starting study drug. Erythropoietin or darbepoetin therapy, if initiated before enrollment, may be continued 13. Patients who are currently receiving treatment with therapeutic doses of warfarin sodium (Coumadin®) or any other coumarin-derivative anticoagulants 14. Patients who have received 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 medication that has known risk to prolong the QT interval or inducing Torsades de Pointes, and the treatment cannot either be discontinued or switched to a different medication prior to starting study drug 16. Patients who are receiving high to moderate CYP3A inhibitors and inducers as listed in Appendix F 17. Known diagnosis of human immunodeficiency virus (HIV) infection (HIV testing is not mandatory) 18. Known history of active infection with Hepatitis B (e.g., HBsAg reactive), or Hepatitis C (e.g., HCV RNA (qualitative) is detected) 19. Has received a live-virus vaccination within 30 days of planned first dose Note: Seasonal flu vaccines are permitted. 20. Inability to swallow or tolerate oral medication 21. 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 participation and compliance in the trial