Neoadjuvant Atezolizumab-Based Combination Therapy in Men With Localized Prostate Cancer Prior to Radical Prostatectomy

Inclusion Criteria: 1. Histologically confirmed adenocarcinoma of the prostate. a. Subjects with small cell or neuroendocrine PC are not eligible. 2. Eligible for radical prostatectomy as determined by urologic oncology surgeon, and subject consents to proceeding with radical prostatectomy. a. Deemed by urologic oncology surgeon to be appropriate for a "window-of-opportunity"study. 3. Only patients with high-risk disease are eligible for the safety lead-in for each cohort. Patients with intermediate-risk disease will be included after interim analyses is complete for the corresponding cohort and the PI has determined that it is safe to do so. 4. Availability of a representative tumor specimen that is suitable for the planned study analyses, as determined by the Principal Investigator. 1. A formalin-fixed paraffin-embedded (FFPE) tumor specimen in a paraffin block (preferred) or at least 15 slides containing unstained, freshly cut, serial sections should be submitted along with an associated pathology report prior to study treatment. If only 10-14 slides are available, the patient may still be eligible for the study, after Principal Investigator approval has been obtained. 2. If archival tumor tissue is unavailable or is determined to be unsuitable for required testing, tumor tissue must be obtained from a biopsy performed at screening. Refer to Section 6.3 for additional information on tumor specimens collected at screening. 5. Subjects have not received any prior systemic or locally directed therapy for PC (see exclusion criteria). 6. Age \>= 18 years 7. Eastern Cooperative Oncology Group (ECOG) performance status of 0 or 1 8. Requirements for organ and marrow function: * Hemoglobin \>= 9 g/dL * \- Participants must not have been transfused within 2 weeks prior to screening to meet this criterion * Absolute neutrophil count \>= 1,500/microliter (uL) without granulocyte colonystimulating factor support * Absolute lymphocyte count \>= 500/uL * Platelets \>= 100,000/uL without transfusion * Total bilirubin \< 1.5 x institutional upper limit of normal (ULN) (known Gilbert disease: \< 3 x ULN) * Alkaline phosphatase \< 2 x institutional ULN * Aspartate aminotransferase (AST) (serum glutamic-oxaloacetic transaminase (SGOT)) =\< 2 x institutional ULN * Alanine aminotransferase (ALT) (serum glutamate pyruvate transaminase (SGPT)) =\< 2 x institutional ULN * International normalized ratio (INR) or activated partial thromboplastin time (aPTT) \< 1.5 x institutional ULN for subjects not receiving therapeutic anticoagulation * Creatinine clearance \>= 30 mL/min (calculated using the Cockcroft-Gault formula) * Serum creatinine \<=1.6 mg/dL (141 μmol/L) in female patients and ≤1.9 mg/dL (168 μmol/L) in male patients . Patients with serum creatinine values exceeding limits may be eligible for the study if their estimated glomerular filtration rates (GFR) are \>30 9. Testosterone level \> 150 ng/dL. 10. Contraception: agreement to remain abstinent or use contraceptive measures, and agreement to refrain from donating sperm as defined below: 1. With female partners of childbearing potential: men must remain abstinent or use a condom plus an additional contraceptive method that together result in a failure rate of \< 1% per year during the treatment period and for 4 months after the last dose of study treatment. Men must refrain from donating sperm during the same period 2. With pregnant female partners: men must remain abstinent or use a condom during the treatment period and for 4 months after the last dose of study treatment to avoid exposing the embryo 3. Abstinence: 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 postovulation methods) and withdrawal are not acceptable methods of contraception 11. For patients receiving therapeutic anticoagulation: stable anticoagulant regimen \> 3 months. 12. Ability to understand a written informed consent document, and the willingness to sign it. 13. Ability to comply with the study protocol, in the investigator's judgment. Exclusion Criteria: 1. Evidence of metastatic disease as determined by standard staging scans. a. Staging scans should be performed per urologic standard of care for patients undergoing radical prostatectomy \[per American Urological Association (AUA)/National Comprehensive Cancer Network (NCCN) guidelines\]. 2. Not a candidate for radical prostatectomy as determined by treating urologic oncology surgeon. 3. Any prior systemic therapy for PC, including antiandrogens, androgen deprivation therapy \[gonadotropin-releasing hormone (GnRH) agonist or antagonist\], chemotherapy, targeted therapy, immunotherapy, OR radiopharmaceuticals. a. Subjects who are on finasteride or dutasteride must discontinue therapy and undergo a washout period of 6 weeks to become eligible for the study. Screening procedures should begin following the washout period. 4. Prior radiotherapy for PC. 5. Any history of prior malignancy, except: 1. Non-melanoma skin cancer treated with curative intent 2. Carcinoma-in-situ (CIS) treated with curative intent, without evidence of recurrence or disease progression for 3 years 3. Appropriately treated Stage I uterine cancer 4. All other cancer: treated with curative intent and without evidence of disease on standard of care follow-up for 5 years 6. 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, Sjogren's syndrome, Guillain-Barre syndrome, or multiple sclerosis, with the following exceptions: 1. Subjects with a history of autoimmune-related hypothyroidism who are on thyroid-replacement therapy, with a stable dose \> 3 months, are eligible for the study 2. Subjects with controlled type 1 diabetes mellitus who are on an insulin regimen, with a Glycated hemoglobin (hemoglobin A1C) \< 7.0 are eligible for the study. All subjects with controlled type 2 diabetes mellitus are eligible for the study 3. Subjects with eczema, psoriasis, lichen simplex chronicus, or vitiligo with dermatologic manifestations only (e.g., patients with psoriatic arthritis are excluded from the study) are eligible for the study provided all of the following conditions are met: * Rash covers \< 10% of body surface area * Disease is well controlled at baseline and requires only low-potency topical steroids * 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 7. History of idiopathic pulmonary fibrosis, organizing pneumonia (e.g., bronchiolitis obliterans), drug-induced pneumonitis, or idiopathic pneumonitis, or any evidence of active, non-infectious pneumonitis requiring corticosteroids. 8. History of prior positive human immunodeficiency virus (HIV) test. 9. Active hepatitis B virus (HBV) or hepatitis C virus (HCV) infection (chronic or acute). 1. Subjects with a past or resolved HBV infection are eligible for this study. 2. HCV positivity is defined as having a positive HCV antibody test followed by a positive HCV ribonucleic acid (RNA) test at screening; the HCV RNA test will only be performed for subjects who have a positive HCV antibody test. 10. Significant cardiovascular disease, such as New York Heart Association class III or greater cardiac disease, myocardial infarction, or cerebrovascular accident within 3 months prior to initiation of study treatment, unstable arrhythmia, or unstable angina. 11. Active chronic obstructive pulmonary disease (COPD) requiring use of home oxygen (O2) or systemic steroid therapy \> 10 mg prednisone (or equivalent) daily. 12. Asthma requiring systemic corticosteroids \> 10 mg prednisone (or equivalent) daily. Inhaled corticosteroids for the treatment of asthma are permitted. 13. Major surgical procedure (including joint surgery) other than for diagnosis within 4 weeks prior to initiation of study treatment, or anticipation of need for a major surgical procedure during the course of the study. a. Placement of central venous access catheter (e.g., port or similar) is not considered a major surgical procedure and is therefore permitted. 14. Severe infection within 4 weeks prior to initiation of study treatment, including, but not limited to, hospitalization for complications of infection, bacteremia, or severe pneumonia. 15. 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. 16. Prior allogeneic stem cell or solid organ transplantation. 17. 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. Note: Because IL-6 inhibition may interfere with the normal immune response to new antigen, patients should be brought up to date on all recommended vaccinations, except for live vaccines, prior to initiation of therapy with tocilizumab to maximize vaccine response. 18. Treatment with investigational therapy within 28 days prior to initiation of study treatment. 19. Prior treatment with adenosine-axis inhibitors, cluster of differentiation 137 (CD137) agonists or immune checkpoint blockade therapies, including anti-cytotoxic T-lymphocyte-associated protein 4 (CTLA-4), ant-PD-1, and anti-PD-L1 therapeutic antibodies. 20. Treatment with systemic immunostimulatory agents \[including, but not limited to, interferon and interleukin 2 (IL-2)\] within 4 weeks or five half-lives of the drug (whichever is longer) prior to initiation of study treatment. 21. Treatment with systemic immunosuppressive medication (including, but not limited to, corticosteroids, cyclophosphamide, azathioprine, methotrexate, thalidomide, and anti-tumor necrosis factor (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: 1. Patients who receive 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 2. Patients who receive mineralocorticoids (e.g., fludrocortisone), corticosteroids for chronic obstructive pulmonary disease (COPD) or asthma (=\< 10 mg prednisone or equivalent), or low-dose corticosteroids for orthostatic hypotension or adrenal insufficiency (=\< 10 mg prednisone or equivalent) are eligible for the study. 22. History of severe allergic anaphylactic reactions to chimeric or humanized antibodies or fusion proteins. 23. Known hypersensitivity to Chinese hamster ovary cell products or to any component of the atezolizumab formulation. 24. Known allergy or hypersensitivity to any of the study drugs of their excipients. 25. Previous treatment with any cell-depleting therapies, including investigational agents or approved therapies, some examples include: CAMPATH, anti-cluster of differentiation 4 (CD4), anti-cluster of differentiation 5 (CD5), anti-cluster of differentiation 3 (CD3), anti-Cluster of Differentiation 19 (CD19) and anti-Cluster of Differentiation 20 (CD20) within 5 years prior to first dose of study treatment. 26. Treatment with intravenous gamma globulin, plasmapheresis or Prosorba column within 6 months of baseline. 27. Previous treatment with tocilizumab (an exception to this criterion may be granted for single dose exposure upon application to the Sponsor-Investigator on a case-by-case basis). 28. Any previous treatment with alkylating agents such as chlorambucil, or with total lymphoid irradiation within 5 years prior to first dose of study treatment. 29. History of severe allergic or anaphylactic reactions to human, humanized or murine monoclonal antibodies. 30. Evidence of serious uncontrolled concomitant, nervous system, pulmonary, renal, hepatic, endocrine (include uncontrolled diabetes mellitus) or gastrointestinal disease (including complicated diverticulitis, ulcerative colitis, or Crohn's disease). 31. Any history of recent serious bacterial, viral, fungal, or other opportunistic infections. 32. Primary or secondary immunodeficiency (history of or currently active) unless related to primary disease under investigation. 33. Any medical or psychological condition that in the opinion of the principal investigator would interfere with safe completion of the trial. 34. Pregnant women or nursing (breast feeding) mothers. 35. Neuropathies or other conditions that might interfere with pain evaluation unless related to primary disease under investigation. 36. Patients with lack of peripheral venous access Additional Exclusion Criteria for Cohort B (atezolizumab + etrumadenant): 37. Treatment with known P-glycoprotein (P-gp) substrates with a narrow therapeutic window, administered orally (e.g., digoxin) within 4 weeks (for investigational drugs when half-life is unknown or not accurately determined) or 5 drug-elimination half-lives of the drug (when half-life is determined), whichever is longer, or if it is a marketed drug, then 5 drug-elimination half-lives of the drug, prior to initiation of study treatment. 38. Treatment with known strong CYP3A4 inducers (e.g., rifampin, phenytoin, carbamazepine, phenobarbital, and St. John's Wort) and strong CYP3A4 inhibitors (eg,clarithromycin, grapefruit juice, itraconazole, ketoconazole, posaconazole, telithromycin,and voriconazole) within 4 weeks (for investigational drugs when half-life is unknown or not accurately determined) or 5 drug-elimination half-lives of the drug (when half-life is determined), whichever is longer, or if it is a marketed drug, then 5 drug-elimination half-lives of the drug, prior to initiation of study treatment. 39. Treatment with known breast cancer resistance protein (BCRP) substrates with a narrow therapeutic window, administered orally (e.g., prazosin, rosuvastatin) within 4 weeks (for investigational drugs when half-life is unknown or not accurately determined) or 5 drug-elimination half-lives of the drug (when half-life is determined), whichever is longer, or if it is a marketed drug, then 5 drug-elimination half-lives of the drug, prior to initiation of study treatment. Additional Exclusion Criteria for Cohort C (atezolizumab + tocilizumab): 40. Known active infection or history of recurrent bacterial, viral, fungal, mycobacterial or other infections, including, but not limited to, TB (i.e., has signs and symptoms of TB) and atypical mycobacterial disease, hepatitis B and C, and herpes zoster, but excluding fungal infections of nail beds.