Combining a new immunotherapy with radiation for prostate cancer treatment

* INCLUSION CRITERIA:
* Participants must have histologically or cytologically confirmed localized intermediate or high risk prostate cancer:

  * Intermediate risk - Gleason 7 disease, PSA less than 10
  * High Risk - Gleason 8-10, PSA\>10, Extracapsular Extension
* Participants must require treatment with SBRT to the prostate and ADT.
* Pre-treatment tissue availability (collected \<= 1 year to initiation of study therapy) for biomarker analysis is mandatory for enrollment. If tissue is determined to be of insufficient/unsuitable quality/quantity, a pre-treatment biopsy prior to initiation of study therapy will be required.
* Male age \>= 18 years old
* ECOG performance status \< 2
* Participants must have adequate organ and marrow function as defined below:

  * absolute neutrophil count \>= 1,500/mcL, without CSF support
  * platelets \>= 100,000/mcL
  * AST(SGOT)/ALT(SGPT) \<= 2.5 X institutional upper limit of normal
  * Hgb \>= 10g/dL (pRBC transfusions are not allowed to achieve acceptable Hgb)
  * Total bilirubin \<= 1.5 x upper limit of normal (ULN),

OR

in participants with Gilbert s syndrome, a total bilirubin \<= 3.0

* Serum albumin \>= 2.8 g/dL
* Creatine \<= 1.5 X institutional ULN

OR

* Creatinine clearance \>= 50 mL/min/1.73 m\^2 for participants with creatinine levels above institutional normal by 24h urine
* PT/INR and aPTT \<= 1.5 X institutional ULN

  * Testosterone greater than 100 ng/dL.
  * Men must agree to use adequate contraception (hormonal or barrier method of birth control; abstinence) after study entry and for 6 months after completion of radiation treatment or immunotherapy (if taken, whatever is last)
  * Participants must have prostate cancer accessible for biopsy
  * Ability of participant to understand and the willingness to sign a written informed consent document.

EXCLUSION CRITERIA:

* Evidence of distant metastatic disease (including clinically or pathologically positive lymph nodes or metastatic disease outside of the pelvis).
* Previous prostatectomy, focal therapy, or radiation to the prostate. Note: Previous finasteride, dutasteride, bicalutamide are allowed at PI discretion.
* Initiation of ADT or SBRT or pelvic nodal radiation irradiation prior to trial enrollment (no time limit).
* Live vaccine therapies for the prevention of infectious disease within 30 days prior to treatment administration. Seasonal flu vaccines that do not contain a live virus are permitted. Locally approved COVID vaccines are permitted.
* Contraindication to mpMRI including allergy or sensitivity to contrast agents (which cannot be alleviated by premedication)
* Contraindications for SBRT such as: rectal wall invasion, history of inflammatory bowel disease, prior radiation in the treatment field that would exceed tissue tolerance.
* Medical comorbidities that preclude the administration of androgen deprivation therapy or uncontrolled chronic or acute intercurrent illness /social situations or other illnesses considered by the Investigator as high risk for investigational drug treatment
* Participants with active immune deficiencies, chronic inflammatory conditions, active autoimmune diseases, or participants on chronic immunosuppressive therapy for whom the primary endpoint of immune response could be impacted.
* Participants requiring requiring systemic corticosteroids (\>10 mg daily prednisone equivalent) or immunosuppressive medications except inhaled steroids and adrenal replacement steroid doses up to 10 mg daily prednisone equivalents are permitted in the absence of active autoimmune disease. Participants with a history of autoimmunity that has not required systemic immunosuppressive therapy or dose not threaten vital organ function including CN, heart, lungs, kidneys, skin and GI track will be allowed
* Participants with HIV
* Active Hepatitis B or Hepatitis C infection
* Significant acute or chronic infections including tuberculosis (history of exposure or history of positive tuberculosis test; plus, presence of clinical symptoms, physical or radiographic findings)
* History of allergic reactions attributed to compounds of similar chemical or biologic composition to PDS01ADC.
* Participants with prior malignancy active within the previous 3 years except for locally curable cancers that have been apparently cured such as basal or squamous cell skin cancer, superficial bladder cancer, or carcinoma in situ of the cervix, breast or low risk Gleason 6 prostate cancer.