Neoantigen DNA Vaccine in Combination With Nivolumab/Ipilimumab and PROSTVAC in Metastatic Hormone-Sensitive Prostate Cancer

Inclusion Criteria: * Histologically confirmed adenocarcinoma of the prostate. * High risk/volume metastatic disease, as defined by 4 or more sites of disease or the presence of visceral metastases. * Must have completed an adequate course of chemo-hormonal, first line therapy for metastatic hormone-sensitive prostate cancer, as determined by the investigator. Patients must remain on stable dose of ADT with castrate levels of testosterone (defined as testosterone \< 50 ng/dL) * At least 18 years of age. * PSA may be undetectable after initial chemo-ADT. * ECOG performance status ≤ 2 * Normal bone marrow and organ function as defined below: * Leukocytes ≥ 2,000/ul * Absolute neutrophil count ≥ 1,500/ul * Platelets ≥ 100,000/ul * Hemoglobin ≥ 9.0 g/ul * Total bilirubin ≤ 1.5 x ULN (except subjects with Gilbert's syndrome who must have a total bilirubin level of ≤ 3.0 ULN) * AST(SGOT) ≤ 3.0 x ULN * ALT(SGPT) ≤ 3.0 x ULN * Creatinine ≤ 1.5 x ULN OR calculated creatinine clearance ≥ 40 mL/min using the Cockcroft-Gault formula * Ability to understand and willingness to sign an IRB approved written informed consent document (or that of legally authorized representative, if applicable). * Must have a biopsy of a metastatic site of disease (may be archival) available and adequate for evaluation and determination of neoantigens by genomic analyses. * Must have all AEs resolved to baseline prior to chemo-ADT, or if treatment related, resolved to grade 1 prior to enrollment. Exclusion Criteria: * Significant small cell or neuroendocrine component or histology, as determined by the institution's reading pathologist. * Progression of disease as defined by a rising PSA (3 sequential values, at least 1 week apart) or radiographic progression based on RECIST1.1 or PCWG3 criteria. * Prior treatment with a checkpoint inhibitor, neoantigen vaccine, or PROSTVAC. * Participants with active, known or suspected autoimmune disease. Participants with type I diabetes mellitus, hypothyroidism only requiring hormone replacement, skin disorders (such as vitiligo, psoriasis, or alopecia) not requiring systemic treatment are permitted to enroll. * Diagnosis of atopic dermatitis or other active exfoliative skin condition * History of concurrent second cancers requiring active, ongoing systemic treatment * Currently receiving any other investigational agents. * Known brain metastases. Prostate cancer patients with known brain metastases must be excluded from this clinical trial because of their poor prognosis, and because they often develop progressive neurologic dysfunction that would confound the evaluation of neurologic and other adverse events. * A history of allergic reactions attributed to compounds of similar chemical or biologic composition to anti-PD-1, anti-CTLA-4, Prostvac-VF Tricom, DNA vaccines, or other agents used in the study. * Prior allergy or significant systemic reaction to vaccinia. * Prior reactions to monoclonal antibodies. * Received hematopoietic stem cell transplant \< 24 months prior to enrollment to this study, or received hematopoietic stem cell transplant ≥ 24 months prior to enrollment to this study but has graft-versus-host disease or disease relapse. * Uncontrolled intercurrent illness including, but not limited to, ongoing or active infection, clinically significant congestive heart failure (NYHA Class III, IV), unstable angina pectoris, cardiac arrhythmia, or psychiatric illness/social situations that in the opinion of the investigator would limit compliance with study requirements. * Immunosuppressed status (e.g. HIV/AIDS, active HCV/HBV, high dose systemic steroids, etc.) as determined by the investigator; topical or inhaled steroids are acceptable. * History of syncopal or vasovagal episode as determined by medical record and history in the 12 month period prior to first vaccination administration. * Individuals in whom a skinfold measurement of the cutaneous and subcutaneous tissue for eligible injection sites (left and right medial deltoid region) exceeds 40 mm. * Individuals in whom the ability to observe possible local reactions at the eligible injection sites (deltoid region) is, in the opinion of the investigator, unacceptably obscured due to a physical condition or permanent body art. * Therapeutic or traumatic metal implant in the skin or muscle of either deltoid region. * Any chronic or active neurologic disorder, including seizures and epilepsy, excluding a single febrile seizure as a child. * Current use of any electronic stimulation device, such as cardiac demand pacemakers, automatic implantable cardiac defibrillator, nerve stimulators, or deep brain stimulators.