Open Label Phase 2 Basket Trial With Atezolizumab and Tiragolumab in Solid Tumors

Inclusion Criteria: * Tumor lesion(s) of which a histological biopsy can be safely obtained according to standard clinical care procedures. * Measurable disease, as defined by RECIST v1.1. Previously irradiated lesions should be discarded as target lesions. * Participate in the GE-269-001 CD8 investigational imaging trial provided that there are slots is that trial. * Signed informed consent. * Age ≥18 at the time of signing informed consent. * Life expectancy ≥12 weeks. * Eastern Cooperative Oncology Group (ECOG) performance status 0-1 * Adequate organ and bone marrow function defined as: 1. hemoglobin ≥9.0 g/dL 2. platelet count ≥100 x 109 / 3. serum creatinine ≤1.5 x upper limit of normal (ULN) or estimated glomerular filtration rate \> 30 mL/min/1.73 m2. A 24-hour urine creatinine collection may substitute for the calculated creatinine clearance to meet eligibility criteria. * Adequate hepatic function defined as: 1. total bilirubin ≤1.5 x ULN (≤3 x ULN if liver tumor involvement); Patients with Gilbert's syndrome do not need to meet total bilirubin requirements, provided their total bilirubin is unchanged from their baseline. Gilbert's syndrome must be documented appropriately as past medical history, 2. aspartate aminotransferase (AST) ≤2.5 x ULN (≤5 x ULN if liver tumor involvement) 3. alanine aminotransferase (ALT) ≤2.5 x ULN (≤5 x ULN if liver tumor involvement) 4. alkaline phosphatase (ALP) ≤2.5 x ULN (≤5 x ULN if liver or bone tumor involvement). * Ability to comply with the protocol. * For female patients of childbearing potential and male patients with partners of childbearing potential, agreement (by the patient and/or partner) to use a highly effective form(s) of contraception (i.e., one that results in a low failure rate (\< 1% per year) when used consistently and correctly). * For the head and neck squamous cell carcinoma cohort specific eligibility criteria apply: 1. clinical T2-4a, or node positive resectable HPV-unrelated HNSCC (oral cavity, larynx, hypopharynx, p16-negative oropharynx or p16 negative unknown primary) 2. no evidence of distant metastases 3. no previous RT to the head and neck region Exclusion criteria: * Signs or symptoms of infection within 2 weeks prior to atezolizumab and tiragolumab administration. * Prior immune checkpoint inhibitor treatment, including but not limited to anti-PD1 and anti-PD-L1 antibodies (only for cohort 1, 2 and 4). * History of severe allergic, anaphylactic, or other hypersensitivity reactions to chimeric or humanized antibodies or fusion proteins. * Any other diseases, metabolic dysfunction, physical examination finding, or clinical laboratory finding giving reasonable suspicion of a disease or condition that contraindicates the use atezolizumab and tiragolumab, or that may affect the interpretation of the results or render the patient at high risk from complications. * Pregnant or lactating women. * Positive test for HIV, active hepatitis B (chronic or acute defined by positive hepatitis B surface antigen (HBsAg) during screening) or hepatitis C. Patients with a medical history of hepatitis B infection (defined as a positive hepatitis B core antibody (HBcAb) and absence of an HBsAg) are eligible for this study. Patients who test positive for hepatitis C antibodies are only eligible with a negative hepatitis C RNA PCR. * Acute or chronic active Epstein-Barr virus (EBV) infection at screening EBV status should be assessed by EBV serology (e.g., anti-VCA IgM and IgG, anti-EA IgG, anti-EBNA IgG) and EBV PCR (plasma or serum). If EBV serology results indicate prior EBV infection, patients must have a negative EBV PCR (plasma or serum) to be eligible for the study. * Active tuberculosis. * Treatment with systemic immunostimulatory agents (including but not limited to IFNs, IL-2) within 6 weeks or five half-lives of the drug, whichever is shorter, prior to the first full dose of atezolizumab and tiragolumab. * Treatment with systemic immunosuppressive medications (including but not limited to prednisone, cyclophosphamide, azathioprine, methotrexate, thalidomide, and anti-tumor necrosis factor agents) within 2 weeks prior to cycle 1, day 1, with the exception of inhaled corticosteroids for chronic obstructive pulmonary disease, mineralocorticoids (e.g., fludrocortisone) for subjects with orthostatic hypotension, low-dose supplemental corticosteroids for adrenocortical insufficiency and topical steroids are allowed. Medications (e.g., a one-time dose of dexamethasone for nausea) may be allowed in the study after discussion with and approval by the principal investigator. * Brain metastases and leptomengeal metastases.