IL-15 Superagonist With or Without Vaccine in Biochemically Recurrent Prostate Cancer After Previous Stereotactic Body Radiation Therapy

Background: * Biochemical recurrence (BCR) denotes rising prostate serum antigen (PSA) and negative computed tomography (CT) and Tc99 bone scan following radical prostatectomy and/or definitive local radiation. * Beyond local salvage radiation options, the management of BCR has not been clearly defined. * As BCR is an asymptomatic stage of disease which can take years to progress to overt metastatic disease, treatment for this stage should have minimal side effects and only be for a limited duration of time. * The advent of prostate-specific membrane antigen (PSMA)-based imaging has driven stereotactic body radiation therapy (SBRT) in BCR despite lack of robust evidence. * Further study is required to ascertain the role of SBRT in BCR. * Due to the presence of only microscopic disease, BCR may be the ideal stage of the disease to evaluate immunotherapy. * Previous studies in the GMB have demonstrated that vaccine can lead to delayed declines in PSA. * N-803 is an IL-15 superagonist which increases the number of natural killer (NK) and CD8 T cells without expanding regulatory T-cells. The net effect is to increase the inflammatory milieu of the tumor microenvironment and this is FDA approved for the treatment of superficial bladder cancer. There is clinical evidence of the activity of N-803 in prostate cancer. * The ETBX-071 is an adenoviral-based vaccine against PSA. * We have previously demonstrated the effects of vaccine in BCR. N-803 has demonstrated preclinical synergy with vaccine and has also been associated with PSA declines in a combination immunotherapy trial in metastatic prostate cancer. Objectives: -To estimate efficacy of N-803 alone or with ETBX-071 vaccine, each administered for 6 months, in participants with biochemically recurrent prostate cancer following PSA progression after SBRT Eligibility: * Biochemically recurrent prostate cancer, defined as PSA over 0.8 ng/ml following radical prostatectomy or \>= 2 ng/ml above the nadir following definitive radiotherapy. * No evidence of soft tissues disease on CT scan and bone metastasis on technetium-99m (Tc99) bone scan. * PSA rise of at least 25% of nadir following prior SBRT treatment for recurrent prostate cancer * Eastern Cooperative Oncology Group (ECOG) performance score 0-1. * No active or organ-threatening autoimmune disease. Design: * This is an open-label phase 2 study in which all participants have received prior SBRT and experienced subsequent PSA progression. * Participants will be randomized between two treatments: N-803 for 6 months versus N-803 with ETBX-071 vaccine for 6 months.