Atezolizumab Plus Tivozanib in Immunologically Cold Tumor Types

Inclusion Criteria: * Subjects must have had at least one prior treatment with systemic therapy for advanced and unresectable, or metastatic disease OR is intolerant to, has refused or for whom there are no standard therapies that impart significant clinical benefit in the opinion of the treating investigator. * An Eastern Cooperative Oncology Group (ECOG) Performance Status less than or equal to 1 for phase 1B. An ECOG Performance Status less than or equal to 2 for phase 2. * Subjects must not have more than one malignancy at the time of enrollment * Adult subjects ≥ eighteen years of age * A clinical diagnosis consistent with stage IV "immunogenically cold" or otherwise incurable cancer of one of the following histologies: i) bile duct or gallbladder cancer ii) Metastatic breast cancer, HR-negative HER2-positive, who have received at least 3 lines of therapy for disease progression that includes: trastuzumab, pertuzumab/trastuzumab, and ado-trastuzumab emtansine iii) neuroendocrine cancer with the following pathological characteristics: grade 2 or 3; well- or moderately- differentiated (Grades 1, 4, and poorly differentiated neuroendocrine pathologies are not eligible) iv) FIGO stage IV or metastatic (using 2021 FIGO classification) high grade serious or high grade endometrioid (based on local histopathological findings) ovarian cancer, primary peritoneal cancer and / or fallopian-tube cancer that is platinum resistant, with no acceptable standard of care v) pancreatic adenocarcinoma vi) soft tissue sarcoma vii) prostate cancer subjects who are castrate-resistant (testosterone ≤ 50 ng/dL) and have progressed on, declined, or are intolerant to other standard of care therapies. Subjects with prostate cancer must have failed at least one line of treatment with an androgen inhibitor (AI) (i.e. enzalutamide, abiraterone, etc.) or cytotoxic chemotherapy in the advanced or metastatic setting viii) vulvar cancer * Adequate hematologic and end-organ function * Subjects receiving therapeutic anticoagulation must be on a stable anticoagulant regimen for ≥ 2 weeks at start of protocol treatment * Negative hepatitis B surface antigen (HBsAg) test at screening * Negative HIV test at screening with the following exceptions: subjects with a positive HIV test at screening are eligible only if they meet the following three conditions: 1) Are stable on anti-retroviral therapy 2) Have a CD4 count ≥ 200/uL AND 3) Have an undetectable viral load. * Women of childbearing potential (WOCBP) must be using an adequate method of contraception (with a failure rate of \<1% per year) to avoid pregnancy throughout the study and for at least 160 days after the last dose of either study drug to minimize the risk of pregnancy. * Males with female partners of child-bearing potential must agree to use physician-approved contraceptive methods throughout the study and should avoid conceiving children for 160 days following the last dose of study drug. * Measurable disease by RECIST criteria * A life expectancy of ≥ 12 weeks * Written informed consent obtained from the subject and the subject agrees to comply with all the study-related procedures * Must have formalin-fixed paraffin embedded (FFPE) tissue or 12 unstained slides available for research purposes. Tissue must have been obtained within the last 3 years. * If a new biopsy is needed for diagnostic reasons, the biopsy must be performed from a tumor site that is not the only site of measurable disease * Subject must be able to swallow capsules Exclusion Criteria: * Subjects with known MSI-H or dMMR tumor status * Subjects with severe uncontrolled hypertension as defined as systolic blood pressure \> 150 mmHg or diastolic blood pressure \> 100 mmHg * Subjects who have had prior treatment with vascular endothelial growth factor receptor (VEGFR) tyrosine kinase inhibitors * Females or males of childbearing potential who are unwilling or unable to use an acceptable method to avoid pregnancy for the entire study period and for at least 160 days after the last dose of study drug * Females who are pregnant or breastfeeding * History of leptomeningeal disease * Uncontrolled or symptomatic hypercalcemia (ionized calcium \> 1.5 mmol/L, calcium \> 12 mg/dL or corrected serum calcium \> ULN) * Uncontrolled tumor-related pain * Uncontrolled pleural effusion, pericardial effusion, or ascites requiring recurrent drainage procedures (once monthly or more frequently, except in the case of ovarian cancer with ascites, which may require more frequent drainage). Subjects with indwelling catheters are allowed. * 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 syndrome, Guillain-Barré syndrome, or multiple sclerosis, with the following exceptions: 1. subjects with a history of autoimmune-related hypothyroidism who are on thyroid-replacement hormone are eligible for the study. 2. subjects with controlled Type 1 diabetes mellitus who are on an insulin regimen are eligible for the study. 3. subjects with eczema, psoriasis, lichen simplex chronicus, or vitiligo with dermatologic manifestations only (e.g., subjects 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 lowpotency topical corticosteroids * There has been 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 * History of idiopathic pulmonary fibrosis, organizing pneumonia (e.g., bronchiolitis obliterans), drug