This is a Phase II, two part trial (A and B), open label study of Atezolizumab and tiragolumab, or atezolizumab combined with SOC chemotherapy in patients with NSCLC or advanced solid tumors that have had prior treatment with a PD-1 inhibitor (e.g. nivolumab or pembrolizumab).

Arm A consists of approximately 20 patients with advanced NSCLC who received first-line anti-PD-1 therapy, who have subsequent disease progression. Arm B consists of approximately 15 patients per disease type (renal cell carcinoma [RCC] progressing on prior anti-PD-1 therapy, triple negative breast cancer [TNBC] progressing on prior anti-PD-1 therapy, NSCLC progressing on check-point inhibitors plus chemotherapy in the first-line setting; and microsatellite instability-high [MSI-high] solid tumors [as determined by local testing for MSI/mismatch repair (MMR)] progressing on prior anti-PD-1 therapy).

Inclusion Criteria:

1. Eastern Cooperative Oncology Group (ECOG) Performance Status score of 0 - 2

2. Adequate hematologic function defined as:

   - Absolute neutrophil count (ANC) ≥1500/μL with one exception: Patients with benign ethnic neutropenia (BEN): ANC >1300/ μL

   - Lymphocyte count ≥0.5 × 109/L (500/µL)

   • Hemoglobin (Hgb) ≥9 g/dL (patients may be transfused to meet this criterion)
   • Platelets ≥100,000/µL (without transfusion, within 7 days of enrollment)

3. Adequate liver function defined as:

   - Alanine aminotransferase (ALT) and aspartate aminotransferase (AST) ≤2.5 x the upper limit of normal (ULN)

   - Total bilirubin ≤1.5 x ULN (patients with known Gilbert syndrome: serum bilirubin level ≤ 3 x ULN)

4. Adequate renal function defined as serum creatinine ≤1.5 mg/dL (133 μmol/L) or calculated creatinine clearance ≥30 mL/min as calculated by the Cockcroft Gault formula

5. For patients not receiving therapeutic anticoagulation: INR or aPTT ≤1.5 × ULN. For patients receiving therapeutic anticoagulation: stable anticoagulant regimen.

6. For women of childbearing potential: agreement to remain abstinent (refrain from heterosexual intercourse) or use contraceptive methods with a failure rate of <1% per year, during their participation in the study and for 5 months following last dose of study drug(s).

   - A woman is considered to be of childbearing potential if she is postmenarchal, has not reached a postmenopausal state (≥12 continuous months of amenorrhea with no identified cause other than menopause), and has not undergone surgical sterilization (removal of ovaries and/or uterus). The definition of childbearing potential may be adapted for alignment with local guidelines or requirements.

   - Examples of contraceptive methods with a failure rate of <1% per year include bilateral tubal ligation, male sterilization, hormonal contraceptives that inhibit ovulation, hormone-releasing intrauterine devices, and copper intrauterine devices. The reliability of sexual abstinence should be evaluated in relation to the duration of the clinical trial and the preferred and usual lifestyle of the patient. Periodic abstinence (e.g., calendar, ovulation, symptothermal, or post-ovulation methods) and withdrawal are not adequate methods of contraception.

7. Male patients with a female partner of childbearing potential or a pregnant female partner must remain abstinent (refrain from heterosexual intercourse) or use a condom must also refrain from donating sperm during the treatment period and for 5 months after the last dose of study drug. The reliability of sexual abstinence should be evaluated in relation to the duration of the clinical trial and the preferred and usual lifestyle of the patient. Periodic abstinence (e.g., calendar, ovulation, symptothermal or post-ovulation methods) and withdrawal are not adequate methods of contraception. Men must also refrain from donating sperm during their participation in the study

8. Age ≥18 years.

9. Willingness to provide a new pre-treatment tumor biopsy.

10. Willingness and ability to comply with study and follow-up procedures.

11. Ability to understand the nature of this study and give written informed consent.

12. Measurable disease by Response Evaluation Criteria in Solid Tumors (RECIST) v1.1.

13. 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 hemorrhage or spinal cord hemorrhage.

    - 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.

    Inclusion Arm A - Non-small cell lung cancer

14. Advanced squamous or non-squamous NSCLC

15. Disease progression after prior documented clinical benefit, defined as having at least one scan demonstrating at least stable disease (SD), on first-line treatment with anti-PD-1 monotherapy

16. Previously received and tolerated nivolumab or pembrolizumab monotherapy or immunotherapy doublets such as nivolumab/ipilimumab therapy (and was the last therapy prior to enrollment)

17. PD-L1 Tumor Proportion Score >/=1%

    Crossover from Arm A to Arm B

18. Last dose of atezolizumab is >/=21 days

Inclusion Arm B - Advanced solid tumors 19. Patients with advanced RCC progressing on anti-PD-1 therapy, Advanced TNBC progressing on anti-PD-1 therapy, and patients with NSCLC progressing on check-point inhibitors plus chemotherapy in the first-line setting. MSI-high solid tumors as defined by local testing for MSI/MMR will also be included.

20. Evidence of disease progression after receiving clinical benefit, defined as having at least one scan demonstrating at least SD, during most recent PD-1 inhibitor treatment.

Exclusion Criteria:

1. History of severe allergic anaphylactic reactions to chimeric or humanized antibodies or fusion proteins
2. History of any Grade 3 or 4 toxicities to a prior CPI treatment
3. Known hypersensitivity to Chinese hamster ovary cell products or to any component of the atezolizumab or tiragolumab formulations
4. Most recent immunotherapy ≤21 days and ≥ Grade 2 immunotherapy-related side effects, with the exception of alopecia.
5. Use of systemic immunostimulatory agents (including, but not limited to, interferon and interleukin 2 [IL-2]) ≤28 days or 5 half-lives (whichever is shorter) prior to the first dose of study drugs.
6. Treatment with chemotherapy in the first line setting.7. Treatment with investigational therapy within 28 days prior to initiation of study treatment.

8. Treatment with systemic immunosuppressive medication (including, but not limited to, corticosteroids, cyclophosphamide, azathioprine, methotrexate, thalidomide, and anti-TNF- agents) within 2 weeks prior to initiation of study treatment, or anticipation of need for systemic immunosuppressive medication during the course of the study, with the following exceptions:

• Patients who received acute, low-dose systemic immunosuppressant medication or a one-time pulse dose of systemic immunosuppressant medication (e.g., 48 hours of corticosteroids for a contrast allergy) are eligible for the study.

• Patients who received mineralocorticoids (e.g., fludrocortisone), inhaled corticosteroids for chronic obstructive pulmonary disease (COPD) or asthma, or low-dose corticosteroids for orthostatic hypotension or adrenal insufficiency are eligible for the study.

  9. Treatment with a live, attenuated vaccine within 4 weeks prior to initiation of study treatment, or anticipation of need for such a vaccine during the course of the study or within 5 months after the last dose of atezolizumab or tiragolumab 10. Uncontrolled tumor-related pain 11. Treatment with therapeutic oral or IV antibiotics within 2 weeks prior to initiation of study treatment.

• Patients receiving prophylactic antibiotics (e.g., to prevent a urinary tract infection or chronic obstructive pulmonary disease exacerbation) are eligible for the study.

  12. Requirement for use of denosumab during the study. Patients who are receiving denosumab for any reason (including hypercalcemia) must be willing and eligible to receive a bisphosphonate instead while in the study.

  13. Wide field radiotherapy (including therapeutic radioisotopes such as strontium 89) administered ≤28 days or limited field radiation for palliation ≤7 days prior to starting study drug or has not recovered from side effects of such therapy.

  14. Major surgical procedures ≤28 days of beginning study drug, or minor surgical procedures ≤7 days. No waiting required following port-a-cath placement.

  15. Symptomatic, untreated, or actively progressing CNS metastases. Patients who have received radiation or surgery for brain metastases are eligible if therapy was completed at least 2 weeks prior to study entry and there is no evidence of central nervous system disease progression, mild neurologic symptoms, and no requirement for chronic corticosteroid therapy. Anticonvulsant therapy at a stable dose is permitted.

  16. Prior allogeneic stem cell or solid organ transplantation 17. Pregnant or lactating females 18. History of idiopathic pulmonary fibrosis, organizing pneumonia (e.g., bronchiolitis obliterans), drug-induced pneumonitis, or idiopathic pneumonitis, or evidence of active pneumonitis on screening chest computed tomography (CT) scan

• History of radiation pneumonitis in the radiation field (fibrosis) is permitted.

  19. Uncontrolled diabetes mellitus. Patients with Type II diabetes are eligible if they require only oral hypoglycemic agents and fasting blood glucose level is ≤120. Patients with Type I diabetes are eligible if HbA1c is ≤7%.

  20. Significant cardiovascular disease, such as New York Heart Association Class II or greater cardiac disease, myocardial infarction, or cerebrovascular accident within 3 months prior to initiation of study treatment, unstable arrhythmia, or unstable angina (see Appendix B) 21. History of leptomeningeal disease 22. Uncontrolled pleural effusion, pericardial effusion, or ascites requiring recurrent drainage procedures (once monthly or more frequently)

• Patients with indwelling catheters (e.g., PleurX) are allowed. 23. Uncontrolled or symptomatic hypercalcemia (-1.5 mmol/L ionized calcium or calcium -12 mg/dL or corrected serum calcium -ULN).

  24. Active or history of autoimmune disease or immune deficiency, including, but not limited to, myasthenia gravis, myositis, autoimmune hepatitis, systemic lupus erythematosus, rheumatoid arthritis, inflammatory bowel disease, antiphospholipid antibody syndrome, Wegener granulomatosis, Sjögren's syndrome, Guillain-Barré syndrome, or multiple sclerosis (see Appendix F for a more comprehensive list of autoimmune diseases and immune deficiencies), with the following exceptions:

• Patients with a history of autoimmune-related hypothyroidism who are on thyroid-replacement hormone are eligible for the study.

• Patients with controlled Type 1 diabetes mellitus who are on an insulin regimen are eligible for the study

• Patients with eczema, psoriasis, lichen simplex chronicus, or vitiligo with dermatologic manifestations only (e.g., patients with psoriatic arthritis are excluded) are eligible for the study provided all of following conditions are met:

  • Rash must cover ˂ 10% of body surface area

  • Disease is well controlled at baseline and requires only low-potency topical corticosteroids

  • No occurrence of acute exacerbations of the underlying condition requiring psoralen plus ultraviolet A radiation, methotrexate, retinoids, biologic agents, oral calcineurin inhibitors, or high potency or oral corticosteroids within the previous 12 months 25. Serious active infection within 4 weeks of treatment (including but not limited to hospitalization for complications of infection, bacteremia, or severe pneumonia), or another serious underlying medical condition that would impair the ability of the patient to receive protocol treatment.

    26. Known active Hepatitis B (HBV) or C (HCV) infection; HBV and HCV testing is not required as part of this study.

    27. Known history of human immunodeficiency virus (HIV1 or 2); HIV testing is not required as part of this study 28. Positive Epstein-Barr virus (EBV) viral capsid antigen (VCA) immunoglobulin M (IgM) test at screening. An EBV PCR test should be performed as clinically indicated to screen for acute infection or suspected chronic active infection. Patients with a positive EBV PCR test are excluded.

    29. Active tuberculosis 30. In the opinion of the Investigator, any other disease, metabolic dysfunction, physical examination finding, or clinical laboratory finding that contraindicates the use of an investigational drug, may affect the interpretation of the results or may render the patient at high risk from treatment complications 31. Has had malignancies other than NSCLC, RCC, TNBC, or MSI-high solid tumors within 5 years prior to enrollment, with the exception of those with a negligible risk of metastasis or death (e.g., expected 5-year OS >90%) treated with an expected curative outcome (such as adequately treated carcinoma in situs of the cervix, basal- or squamous-cell skin cancer, localized prostate cancer treated surgically with curative intent, or ductal carcinoma in situ treated surgically with curative intent).

    32. Psychological, familial, sociological, or geographical conditions that do not permit compliance with the protocol.

    33. Prior treatment with anti-T-cell immunoreceptor with immunoglobulin and immunoreceptor tyrosine-based inhibition motif domains (TIGIT) therapeutic antibodies.

    34. Major surgical procedure within 4 weeks prior to initiation of study treatment, or anticipation of need for a major surgical procedure during the study.

Exclusion Arm A Non-small cell lung cancer 35. NSCLC with an activating EGFR mutation or ALK fusion oncogene

• For patients with non-squamous NSCLC histology: unknown EGFR and/or ALK status requires testing

• For patients with squamous NSCLC histology: unknown EGFR and/or ALK status does not require test results at screening. However, exclusion is applied if the status of either driver oncogene is known to be positive.

• For patients with NSCLC of mixed histology: unknown EGFR and/or ALK status requires testing at screening Note: ALK and/or EGFR status may be assessed locally or submitted for central laboratory testing. If ALK and/or EGFR status is assessed locally, testing must be performed on tissue or cytology using a validated FDA-approved test. If samples are submitted for central laboratory testing, five additional slides are required.

  36. Known c-ros oncogene 1 (ROS1) rearrangement: ROS1 testing at screening is not required for study inclusion; however, patients with known ROS1 rearrangements are excluded.

  37. Intervening treatment with a regimen other than a checkpoint inhibitor prior to enrollment in this study.

Exclusion Arm B - Advanced Solid Tumors 38. Prior treatment with anti-TIGIT therapeutic antibodies. 39. Known hypersensitivity to any component of the tiragolumab formulation.