Tiragolumab and Atezolizumab in Advanced Pan-cancer Patients

Inclusion Criteria: 1. Provision of written informed consent. 2. Aged ≥18 years old. 3. Histologically or cytologically confirmed locally advanced unresectable or metastatic solid tumour. 4. Exhausted all available standard therapy or not suitable for standard therapy (including targeted therapies) for the tumour. 5. ECOG performance status score of 0-1. 6. Sufficient and accessible tumour tissue for panel sequencing, PD-L1 and TIL testing, and tertiary objectives. 7. Tumour biomarker criteria predictive of immune response defined by presence of one or more of the following; * Group 1: tumour mutation burden ≥ 10 mutations per megabase. * Group 2: PD-L1 amplification \>6 copy number alterations * Group 3: tumour PD-L1 expression TAP score ≥ 5% * Group 4: tumour infiltrating lymphocytes (TILs) (CD3+CD8+) ≥ 5%. 8. Patient is willing to provide tumour biopsy samples on treatment at Week 4. 9. Life expectancy \>12 weeks. 10. Measurable disease as defined by iRECIST or RANO criteria. 11. Adequate haematological and biochemical indices as defined by: * Absolute neutrophil count ≥1.0 x 10\^9/L * Haemoglobin ≥100 g/L * Platelet count ≥100 x 10\^9/L * Serum bilirubin ≤ 1.5 x institutional upper limit of normal (ULN). This will not apply to patients with confirmed Gilbert's syndrome (persistent or recurrent hyperbilirubinemia that is predominantly unconjugated in the absence of haemolysis or hepatic pathology), who will be allowed only in consultation with their physician. * Alanine aminotransferase (ALT) and aspartate aminotransferase (AST) ≤2.5x ULN; or ≤5.0x ULN if liver metastases are present. * International normalised ratio (INR) \<1.3 in the absence of anticoagulation therapy. * Serum creatinine clearance \>40 mL/min by the Cockcroft-Gault formula or by 24-hour urine collection for determination of creatinine clearance. 12. Negative HIV test at screening, with the following exception: patients with a positive HIV test at screening are eligible provided they are stable on antiretroviral therapy, have a CD4 count ≥ 200cells/mm3 , and have an undetectable viral load. 13. Negative hepatitis B surface antigen (HBsAg) test at screening. 14. Positive hepatitis B surface antibody (HBsAb) test at screening, or negative HBsAb at screening accompanied by either of the following: * Negative total hepatitis B core antibody (HBcAb); * Positive total HBcAb test followed by quantitative hepatitis B virus (HBV) DNA \< 500 IU/mL. The HBV DNA test must be performed for patients who have a negative HBsAg test, a negative HBsAb test, and a positive total HBcAb test. 15. Negative hepatitis C virus (HCV) antibody test at screening, or positive HCV antibody test followed by a negative HCV RNA test at screening. The HCV RNA test must be performed for patients who have a positive HCV antibody test. 16. Women of childbearing potential must have a negative screening serum pregnancy test within 14 days prior to the first dose of study medication. 17. Women of childbearing potential and men must remain abstinent or use contraceptive methods with a failure rate of \<1% per year during the study and for at least 5 months after the last dose of study medication. 18. Ability to adhere to the study visit schedule and understand and comply with all protocol requirements and instructions from study staff. Exclusion Criteria: 1. Involvement in the planning and/or conduct of the study (applies to both Roche staff and/or staff at the study site). 2. Patients with non-small cell lung cancer. 3. Participation in another clinical study with an investigational product during the last 4 weeks prior to study enrolment. 4. Any unresolved toxicity (\>CTCAE grade 2) from previous anti-cancer therapy. Patients with irreversible toxicity that is not reasonably expected to be exacerbated by the investigational product may be included (e.g., hearing loss, peripherally neuropathy). 5. Mean QT interval corrected for heart rate (QTc) ≥470 ms calculated from 3 electrocardiograms (ECGs) using Fridericia's Correction. 6. Treatment with systemic immunosuppressive medication (including, but not limited to, corticosteroids, cyclophosphamide, azathioprine, methotrexate, thalidomide, and anti-tumor necrosis factor-α \[TNF-α\] agents) within 2 weeks prior to initiation of study treatment, or anticipation of need for systemic immunosuppressive medication during study treatment, with the following exceptions: * topical, intranasal, or inhaled corticosteroids or systemic corticosteroids at or below physiological doses (eg. ≤10 mg/day of prednisone); * use of dexamethasone up to 4mg/day within 14 days of initial treatment for patients with brain tumours. 7. Symptomatic or actively progressing central nervous system (CNS) metastases. Asymptomatic patients with treated or untreated CNS lesions are eligible, provided that all of the following criteria are met: * Measurable disease, per RECIST v1.1, must be present outside the CNS. * The patient has no history of intracranial haemorrhage or spinal cord haemorrhage. * The patient has not undergone stereotactic radiotherapy within 7 days prior to initiation of study treatment, whole-brain radiotherapy within 14 days prior to initiation of study treatment, or neurosurgical resection within 28 days prior to initiation of study treatment. * The patient has no ongoing requirement for corticosteroids as therapy for CNS disease. * If the patient is receiving anti-convulsant therapy, the dose is considered stable. * Metastases are limited to the cerebellum or the supratentorial region (i.e., no metastases to the midbrain, pons, medulla, or spinal cord). * There is no evidence of interim progression between completion of CNS directed therapy (if administered) and initiation of study treatment. Asymptomatic patients with CNS metastases newly detected at screening are eligible for the study after receiving radiotherapy and/or surg