• Age greater than or equal to 18 years at the time of signature of informed consent.

• Participants with an incurable solid tumour who have undergone whole genome and transcriptome analysis (WGTA) as part of Personalized OncoGenomics (POG) or equivalent program.

• a. Participants must have had successful sequencing of their tumour, been formally reviewed by the POG (or POG-approved) genome analysts and found to have CAPTIV-8 factors identified (including Immune, Burden, Variant (IBV) score ≥ 5), been reviewed at the Molecular Tumour Board (MTB) (or site equivalent), and allocated to a specific tumour-defined cohort (that is open for enrolment) with a final opinion documented.

• Eastern Cooperative Oncology Group (ECOG) performance status 0-2.

• Participants must have measurable disease, as defined by RECIST 1.1.

• Life expectancy of at least 12 weeks.

• Adequate hematologic and end-organ function, as defined by the following laboratory results obtained within 28 days prior to the first study treatment:

‣ Absolute neutrophil count (ANC) ≥ 1500 cells/µL without granulocyte colony- stimulating factor support.

⁃ White blood cell (WBC) counts \> 2500/µL.

⁃ Lymphocyte count ≥ 500/µL.

⁃ Serum albumin ≥ 2.5 g/dL.

⁃ Platelet count ≥ 100,000/µL without transfusion (without transfusion within 2 weeks of laboratory test used to determine eligibility).

⁃ Hemoglobin ≥ 9.0 g/dL, participants may be transfused or receive erythropoietic treatment to meet this criterion.

⁃ International normalized ratio (INR) or activated partial thromboplastin time (aPTT) ≤ 1.5 × Upper Limit of Normal (ULN). This applies only to participants who are not receiving therapeutic anticoagulation; participants receiving therapeutic anticoagulation must have an INR or aPTT within therapeutic limits for at least 1 week prior to enrolment.

⁃ Aspartate aminotransferase (AST), alanine aminotransferase (ALT), and alkaline phosphatase (ALP) ≤ 2.5 × ULN with the following exceptions: i) Participants with documented liver metastases: AST and/or ALT ≤ 5 × ULN. ii) Participants with documented liver or bone metastases: ALP ≤ 5 × ULN.

⁃ Serum bilirubin ≤ 1.5 × ULN. Participants with known Gilbert's syndrome who have serum bilirubin level ≤ 3 × ULN may be enrolled.

‣ Serum creatinine ≤ 1.5 × ULN.

• For women of childbearing potential: agreement to remain abstinent (refrain from heterosexual intercourse) or use contraceptive methods that result in a failure rate of less than 1% (one percent) per year during the treatment period and for at least 5 months after the last dose of atezolizumab.

• For men: agreement to remain abstinent (refrain from heterosexual intercourse with a female partner of childbearing potential or who is pregnant) or use contraceptive measures that result in a failure rate of less than 1% (one percent) per year, and agreement to refrain from donating sperm, during the treatment period and for at least 5 months after the last dose of atezolizumab.

• Asymptomatic participants with treated or untreated CNS lesions are eligible provided that all of the following criteria are met:

‣ Measurable disease, per RECIST 1.1, must be present.

⁃ The participant has no history of intracranial hemorrhage or spinal cord hemorrhage.

⁃ The participant has not undergone stereotactic radiotherapy within 7 days prior to the 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 participant has no ongoing requirement for corticosteroids as therapy for CNS disease. Anticonvulsant therapy at a stable dose is permitted.

• Ability to give informed consent for the study procedures defined in this protocol.