≥ 18 years of age

Arm A：Histopathological or cytologically documented locally advanced or metastatic and solid tumors（including but not limited to advanced cholangiocarcinoma, small cell lung cancer, HER2-negative breast cancer including TNBC, bladder cancer, prostate cancer, thyroid cancer, gastric cancer, gallbladder cancer and other advanced solid tumors.

Arm B：Histopathological or cytologically documented locally advanced or metastatic and Unresectable advanced biliary tract malignant tumors (except ampullary carcinoma).

Arm C： * Histopathological invasive advanced TNBC with triple-negative receptor status that meets the institution standards was proved ER or PR by IHC (positive tumor nucleus\<10% ) * HER2-negative (ASCO-CAP guideline \[Wolff A C, 2018\] )

Received all currently available standard treatments (unless the treatment is contraindicated, intolerable, or unavailable for any reason)

At least one measurable lesion as defined by RECIST V1.1 criteria for solid tumors

Eastern Cooperative Oncology Group (ECOG) performance status ≤ 2

6. Adequate organ and bone marrow function(without receiving any hematopoietic growth factor, blood or platelet therapy within 1 week before the first dose. * Complete blood count (CBC): * Absolute Neutrophil Count (ANC)≥ 1.5 × 109/L * Hemoglobin（Hgb）≥ 9 g/dl * Platelets（Plt）≥ 75 × 109/L * Liver function: * AST/SGOT and ALT/SGPT ≤ 2.5 x Upper Limit of Normal (ULN) or ≤ 5.0 × ULN if liver metastases are present . * Total bilirubin ≤ 1.5 × ULN or direct bilirubin\<ULN (if total bilirubin\>1.5 ULN). * Patients with hepatocellular carcinoma (HCC) and BTC: Child Pugh A or B (Score ≤ 7). * Renal fuction: * serum creatinine ≤ 1.5 × ULN or Calculated 24-hour clearance ≥ 50 mL/min (Cockcroft Gault formula).

Must agree to take sufficient contraceptive methods to avoid pregnancy during the study and until at least 6 months after ceasing study treatment

Able to sign informed consent and comply with the protocol

Patients who meet one or more of the following criteria will not be included in this study:

Women who are pregnant or lactating

Women of child-bearing potential (WOCBP) who do not use adequate birth control

Patients with any hematologic malignancy, including leukemia (any form), lymphoma, and multiple myeloma

Patients with a history of * primary central nervous system tumors or * carcinomatous meningitis (also known as leptomeningeal disease). Note: Patients with treated brain metastases that are off corticosteroids and have been clinically stable for 28 days are eligible for enrollment

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 ≥ 450 msec on screening ECG * Unstable angina pectoris ≤ 3 months prior to starting study drug * Acute myocardial infarction ≤ 3 months prior to starting study dru

Patients who are currently receiving treatment with medication that has known risk to prolong the QT interval or induce Torsades de Pointes, and the treatment cannot either be discontinued or switched to a different medication prior to starting study drug.

Patients with impairment of gastrointestinal (GI) function, or GI disease that may significantly alter the absorption of TT-00420

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

Patients who have undergone major surgery or wide field radiotherapy ≤ 4 weeks prior to starting study drug or who have not recovered from side effects of such therapy

Patients who are currently receiving treatment with strong CYP3A inhibitors or inducers ≤ 2 weeks prior to starting study drug.

Patients who have used of proton pump inhibitors (PPIs) within 4 days or histamine H2 blockers within 2 days prior to starting study drug

Human Immunodeficiency Virus (HIV) positive

Patients with active HBV infection (HBV DNA copy number ≥ ULN) and/or HCV infection (HCV RNA copy number ≥ ULN)

Patients with active tuberculosis

Has received a live-virus vaccination within 30 days of planned first dose Note：Seasonal flu and COVID-19 vaccines are permitted before enrollment at least 7 days.

Patients with a history of medical conditions, treatment, or abnormal laboratory tests that could affect the results of the study, interfere with study participation and compliance per investigator's judgment

【Note】：The following three types of patients may be enrolled after being determined by the sponsor:

①Patients who have received emergency, low-dose, systemic immunosuppressive therapy (for example, one-time dexamethasone administration for vomiting);

② Patients who need steroid prophylaxis and have a history of intravenous contrast agent allergic reactions should use MRI for baseline and follow-up tumor assessment;

③The use of inhaled corticosteroids to treat chronic obstructive pulmonary disease, the use of mineralocorticoids (such as fludrocortisone) to treat patients with orthostatic hypotension and the use of low-dose supplementary corticosteroids to treat adrenal insufficiency are permitted.

Arm B: TT-00420 tablet in combination with Atezolizumab Injection (Tecentriq ®): Subjects who meet one or more of the following criteria are also not allowed to participate in this study.

A history of severe allergies, immune stress, or other hypersensitivity reactions to chimeric or humanized antibodies or fusion proteins.

Known to have hypersensitivity or allergies to any ingredient of Chinese hamster ovary cells or atelizumab injection.

History of autoimmune diseases, including but not limited to myasthenia gravis, autoimmune myositis, autoimmune hepatitis, systemic lupus erythematosus, rheumatoid arthritis, inflammatory bowel disease, and antiphospholipid syndrome related Vascular thrombosis, Wegener's granulomatosis, Sjögren's syndrome, Guillain-Barré syndrome, multiple sclerosis, vasculitis or glomerulonephritis.

【Note】The following two types of patients may be enrolled after being determined by the sponsor: ① Patients who have a history of autoimmune hypothyroidism but have stable doses of thyroid replacement hormone therapy; ② Patients who use stable doses of insulin therapy to control type I diabetes may can be enrolled.

Patients who have a history of allogeneic stem cell or solid organ transplantation.

Patients who have a history of non-specific pulmonary fibrosis, tissue pneumonia (such as: bronchiolitis obliterans, unknown tissue pneumonia), drug-induced pneumonia, or active pneumonia showed by chest CT scan.

【Note】radiation pneumonitis (fibrosis) exist in the radiation area can be enrolled.

Patients who have received systemic immunostimulatory drugs therapy (including but not limited to interferon or IL-2) ≤ the shorter one of 4 weeks or 5 half-lives of immunostimulatory drugs.

Patients who have received systemic corticosteroids or other systemic immunosuppressive drugs (including but not limited to prednisone, dexamethasone, cyclophosphamide, azathioprine, methotrexate, and Tumor Necrosis Factor (TNF)) within 2 weeks prior to starting study.