Multitargeted Recombinant Ad5 PSA/MUC-1/Brachyury-Based Immunotherapy (TriAdeno) Vaccine With IL-15 Superagonist N-803 in Participants With Clinically Localized Prostate Cancer Undergoing Active Surveillance

Background: * Prostate cancer (PCa) is the most common non-cutaneous cancer and second most common cause of cancer-related death among men living in the United States. * With increasing detection of localized, low-grade PCa in the prostate-specific antigen (PSA) screening era, active surveillance of PCa has emerged as a viable management strategy in selected, favorable risk population. Though active surveillance is the preferred management strategy for low-grade PCa and an option for selected favorable, intermediate risk disease according to the National Comprehensive Cancer Network (NCCN), up to 35% of men will need radical therapy within 5 years due to progression of PCa. * Vaccine strategies represent a novel therapeutic approach in the prevention and possible treatment of early-stage PCa. A new trivalent vaccine which targets 3 tumor-associated antigens (PSA, brachyury, and MUC-1) has been shown to induce an immune response in a Phase I study of patients with metastatic castrate-resistant PCa. * N-803 is an IL-15 agonist that activates and expands T cells and NK cells. N-803 enhances anti-tumor activity in combination with tumor-targeted vaccines. Clinically, multiple studies have demonstrated the safety of tumor-targeted vaccine in combination with PD-1/PD-L1 blockade. Adding N-803 to PD-1/PD-L1 blockade can produce antitumor responses in disease states where responses to PD-1/PD-L1 alone would not be expected. * The TriAdeno vaccine has not been evaluated in populations with early stage, low grade PCa. Primary Objective: -To determine the effect of an Ad5 PSA/MUC-1/brachyury-based immunotherapy vaccine (TriAdeno) with IL-15 superagonist N-803 on immune infiltration of the local tumor environment by comparing pre- and post-treatment CD8+ and CD4+ T-cell density within the malignant portion of prostate biopsies in participants on active surveillance for low and intermediate risk prostate cancer Eligibility: * Biopsy-proven, organ confined low or intermediate risk adenocarcinoma of the prostate * Age \>=18 years * Serum PSA \<20 ng/mL (or \<10 ng/mL for participants being treated with 5-alpha-reductase inhibitors) * Eastern Cooperative Oncology Group (ECOG) performance status \<=1 Design: * This is an open-label, non-randomized Phase II trial of TriAdeno vaccine given concurrently with N-803 in participants with localized, early stage, low and intermediate risk PCa on active surveillance. * The TriAdeno vaccines will be administered subcutaneously (SC) at doses of 5x1011 viral particles (VP) on Day 1 of every 21-day cycle for up to four (4) cycles. * N-803 will be administered SC at 15 mcg/kg on Day 1 of every 21-day cycle for up to four (4) cycles. * Up to 49 participants may be treated.