Inclusion Criteria:  ≥ 18 years of age, at the time of signing informed consent  Histologically or cytologically documented advanced/metastatic or surgically unresectable cholangiocarcinoma who have received at least one line of prior systemic chemotherapy. Patients will be assigned to 1 of 4 cohorts:  Cohort A1: FGFR2 fusions who have failed at least one previous treatment with an FGFR inhibitor Cohort A2: FGFR2 fusions who have previously responded on at least one previous treatment with an FGFR inhibitor Cohort B: other FGFR alterations, including FGFR2 mutations and FGFR1/3 alterations, including fusions Cohort C: negative for FGFR alterations (FGFR wild-type) At least one measurable lesion as defined by RECIST V1.1 criteria for solid tumors5 Documentation of FGFR gene alteration status Eastern Cooperative Oncology Group (ECOG) performance status of 0 or 1  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 aspartate aminotransferase/serum glutamate oxaloacetate transaminase (AST/SGOT) and alanine aminotransferase/serum glutamate pyruvate transaminase (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 24-hour clearance ≥ 50 mL/min (Cockcroft Gault formula Negative pregnancy test within 72 hours before starting study treatment in all premenopausal women and women < 12 months after the onset of menopause Must agree to take sufficient contraceptive methods to avoid pregnancy (including male and female participants) during the study and until at least 6 months after ceasing study treatment Able to sign informed consent and comply with the protocol  Exclusion Criteria:  Women who are pregnant or lactating Women of child-bearing potential (WOCBP) who do not use adequate birth control Patients with untreated brain or central nervous system (CNS) metastases or brain/CNS metastases that have progressed (e.g. evidence of new or enlarging brain metastasis or new neurological symptoms attributable to brain/CNS metastases) Note: Patients with treated brain metastases that are off corticosteroids and have been clinically stable for 28 days are eligible for enrollment. Patients with a known concurrent malignancy that is progressing or requires active treatment. Exceptions include basal cell carcinoma of the skin, carcinoma in situ of the cervix or other noninvasive or indolent malignancy that has previously undergone potentially curative therapy.  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  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 Patients with uncontrolled hypertension (defined as blood pressure of ≥ 150 mmHg systolic and/or ≥ 90 mmHg diastolic at Screening)  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. Other concurrent severe and/or uncontrolled concomitant medical conditions (e.g. uncontrolled hypertriglyceridemia [triglycerides > 500 mg/dL], or active or uncontrolled infection) that could cause unacceptable safety risks or compromise compliance with the protocol Patients who have received chemotherapy, targeted therapy, or immunotherapy ≤ 5 half-lives or 3 weeks, whichever is shorter, (6 weeks for nitrosourea or mitomycin-C) prior to starting study drug 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 adverse events of prior therapy Patients who have undergone major surgery ≤ 4 weeks prior to starting study drug or who have not recovered from adverse events of prior therapy Patients who are currently receiving treatment with therapeutic doses of warfarin sodium (Coumadin®) or any other coumarin-derivative anticoagulants Patients who are currently receiving treatment with strong CYP3A inhibitors or inducers ≤ 2 weeks prior to starting study drug. Known diagnosis of human immunodeficiency virus (HIV) infection (HIV testing is not mandatory; patients with well controlled HIV might be enrolled per investigator's discretion and Sponsor approval) Evidence of active infection with Hepatitis B or Hepatitis C that is not adequately controlled. For patients with known prior history of Hepatitis B or Hepatitis C, enrollment may be allowed per investigator's discretion and Sponsor approval. Inability to swallow or tolerate oral medication 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.