Perioperative Atezolizumab With MVA-BN-Brachyury and PROSTVAC For Intermediate-Risk And High-Risk Localized Prostate Cancer

Inclusion Criteria: * Male subjects aged ≥ 18 years. * Clinical staged unfavorable intermediate, high-risk or very high-risk prostate cancer per NCCN guidelines. * Histologically proven prostate adenocarcinoma * Patient must be a surgical candidate * ECOG Performance Status ≤ 1. * Adequate organ function as defined as: * Hematologic: * Absolute neutrophil count (ANC) ≥ 1.5 × 109/L (without granulocyte colony-stimulation factor support within 2 weeks of screening blood test) * Platelet count ≥ 100 × 109/L (without platelet transfusion within 2 weeks of screening) * Hemoglobin ≥ 9 g/dL (may not have been transfused within 2 weeks of study treatment initiation) * White blood cell count (WBC) ≥ 2.5 × 109/L. * Hepatic: * Total bilirubin level ≤ 1.5 × the upper limit of normal (ULN) (≤ 3 × ULN for subjects with Gilbert's disease) * AST and ALT levels ≤ 2.5 × ULN. Patient with a history of unconjugated hyperbilirubinemia with otherwise acceptable liver enzyme levels (as per above criteria) may have higher bilirubin levels. * Renal: * Urine protein/creatinine ratio (UPCR) ≤ 2 mg/mg (≤ 113.2 mg/mmol) UPCR can be calculated with either a random spot urine test or a 24 hour test. The 24-hour urine collection test is more accurate, so it is the definitive test if there is a discrepancy between the urnialysis and the UPCR. A 24-hour urine test is not required, but may be obtained. * Serum creatinine ≤ 2.0 × ULN or calculated creatinine clearance ≥ 30 mL/min (≥ 0.5 mL/sec) using the Cockcroft-Gault equation. * Highly effective contraception for male subjects throughout the study and for at least 6 months after last study treatment administration if the risk of conception exists. * Patients must have archival prostate biopsy tissue available with identified prostate cancer. If none is available, a repeat prostate biopsy is mandatory to be eligible for this study. The repeat biopsy if performed must have documented prostate adenocarcinoma. The archival tissue must not have been obtained more than 4 months before enrollment. * Able to provide informed consent and willing to sign an approved consent form that conforms to federal and institutional guidelines. * Prostate MRI must be performed within the past 8 months. Exclusion Criteria: * Prostate cancer histology other than adenocarcinoma. * Previous treatment for prostate cancer. * Metastatic disease on imaging (CT, MRI, or NM bone scan) or through tissue biopsy. This includes nodal metastatic disease. A biopsy is not required to rule out metastasis. * Use of immunosuppressive medication within 28 days of study treatment initiation, EXCEPT for the following: * Intranasal, inhaled, topical steroids, or local steroid injection (e.g., intra-articular injection); * Systemic corticosteroids at physiologic doses ≤ 10 mg/day of prednisone or equivalent; * Steroids as premedication for hypersensitivity reactions (e.g. CT scan premedication). * Known history of and/or active autoimmune disease requiring systemic treatment. Patients with diabetes mellitus, thyroid disease, vitiligo, or other diseases determined to be not clinically meaningful (per the treating physician) will not be excluded for these conditions. * Active autoimmune disease that might deteriorate when receiving an immuno-stimulatory agent per treating physician's clinical judgment. Subjects with diabetes type I, vitiligo, psoriasis, hypo- or hyperthyroid diseases, or other conditions are eligible as per 5.2.5. * The subject has uncontrolled, significant intercurrent or recent illness including, but not limited to, the following conditions: o Cardiovascular disorders: * Congestive heart failure New York Heart Association Class 3 or 4, unstable angina pectoris, serious cardiac arrhythmias within 3 months of study enrollment. * Uncontrolled hypertension defined as sustained blood pressure (BP) \> 180 mm Hg systolic or \> 120 mm Hg diastolic despite optimal antihypertensive treatment within 2 weeks of starting treatment. * Stroke (including transient ischemic attack \[TIA\]), myocardial infarction (MI), or other ischemic event, or thromboembolic event (eg, deep venous thrombosis, pulmonary embolism) within 3 months before first dose. * Uncontrolled tumor-related pain. * Uncontrolled pleural effusion, pericardial effusion, or ascites requiring recurrent drainage procedures (once monthly or more frequently). * Uncontrolled or symptomatic hypercalcemia (ionized calcium \> 1.5 mmol/L, calcium \> 12 mg/dL or corrected serum calcium \>ULN). * Active Tuberculosis * Prior allogeneic stem cell or solid organ transplantation. * Known history of acquired immunodeficiency syndrome. * Prior or concurrent malignancy whose natural history or treatment, in the opinion of the enrolling investigator, may have the potential to interfere with the safety or efficacy assessment of the investigational regimen. * Known active hepatitis B virus (HBV) or hepatitis C virus (HCV) infection at screening. Patients with a history of HBV or HCV infection are eligible if the viral load is documented as undetectable at screening. Screening tests for HBV, HCV or HIV are not mandatory by the study but will be performed per the discretion of the study investigators. * Known history of atopic dermatitis or active skin condition (acute chronic, or exfoliative) that disrupts the epidermis that is clinically significant less than or equal to 180 days before study enrollment. * Known 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. * Known history of severe allergic anaphylactic reactions to chimeric or humanized antibodies or fusion proteins. * Live, attenuated (e.g., FluMist) and inactive vaccinations within 28 days of study treatment initiation. Live, attenuated vaccinations are generally discouraged for the duration of the investigational treatment phase of the study. Inactive vaccinations are acceptable after the prostatectomy is performed but cannot be given within 1 week of the study vaccine administration. Live vaccinations require PI approval. * Known prior severe hypersensitivity to investigational product or any component in its formulations, including known severe hypersensitivity reactions to monoclonal antibodies (NCI CTCAE v 5.0 Grade ≥ 3). * Known allergy to eggs, egg products, or aminoglycoside antibiotics (for example gentamicin or tobramycin). * Known hypersensitivity to Chinese hamster ovary cell products or to any component of the atezolizumab formulation. * Known allergy or hypersensitivity to any component of the PROSTVAC or MVA-BN-Brachyury formulation. * Subjects taking prohibited medications as described in Section 6.6. A washout period of prohibited medications for a period of at least 14 days or as clinically indicated should occur prior to the start of treatment.