Testing the Combination of Anti-cancer Drugs Atezolizumab and Tiragolumab in People With Advanced Stage Rare Cancers, RARE3 Trial

PRIMARY OBJECTIVE: I. Determine the proportion of activated CD8+ T cells at baseline and after treatment with atezolizumab and tiragolumab. SECONDARY OBJECTIVES: I. Determine the objective response rate (ORR) of patients with advanced rare cancers to the combination of atezolizumab and tiragolumab using Response Evaluation Criteria in Solid Tumors (RECIST) version (v) 1.1 and Immune-Modified (i)RECIST guidelines. II. Measure progression-free survival (PFS) time (time frame: baseline until disease progression, death, loss to follow-up, initiation of another anti-cancer treatment, withdrawal of consent, or study termination). III. Measure the proportion of patients with a clinically promising increase in CD8+ T cell infiltration following treatment with atezolizumab and tiragolumab. EXPLORATORY OBJECTIVES: I. Investigate immune activation markers and the immune composition (regulatory T \[Treg\], natural killer \[NK\], B-cells, macrophages, myeloid-derived suppressor cells \[MDSC\], tumor mutation burden \[TMB\], microsatellite instability \[MSI\]) in tumor microenvironment (TME) before and after study treatment. II. Measure T cell receptor (TCR) signaling in tumor-infiltrating T cells in the TME as well as in circulating T cells in blood before and after study treatment using multiplex immunofluorescence assays (IFAs)-developed by the National Cancer Institute (NCI)-Frederick Pharmacodynamic Assay Development \& Implementation Section (PADIS)-and use these measurements to evaluate the relationship between TCR signaling in circulating T cells and TME. III. Evaluate potential associations between atezolizumab and tiragolumab activity and tumor genomic alterations, genomic expression, or TMB as determined from genomic analysis of biopsy samples. IV. Evaluate genomic alterations in cell free deoxyribonucleic acid (DNA) (cfDNA) and their potential association with therapy response or resistance. V. Evaluate the pharmacodynamic effects of the treatment on biomarkers of cell death and epithelial-to-mesenchymal transition (EMT) in tumor tissue and circulating tumor cells (CTCs). VI. Evaluate markers of immune response and the presence of tertiary lymphoid structures (TLS) in TME at baseline and following atezolizumab plus tiragolumab therapy. OUTLINE: Patients receive atezolizumab intravenously (IV) over 60 minutes and tiragolumab IV over 30-90 minutes on day 1 of each cycle. Cycles repeat every 21 days in the absence of disease progression or unacceptable toxicity. Patients also undergo echocardiography (ECHO) at baseline, undergo biopsy at baseline and on study, and undergo computed tomography (CT) and collection of blood samples throughout the study. After completion of study treatment, patients are followed up for 30 days.