This phase II trial studies how well a short course of androgen deprivation therapy (ADT) with relugolix works in increasing expression of prostate-specific membrane antigen (PSMA) and improving diagnostic imaging with PSMA positron emission tomography (PET)/computed tomography (CT) in patients with high risk or very high risk prostate cancer. PSMA PET/CT has become the standard of care in imaging for high-risk prostate cancer. However, a limitation of PSMA PET/CT is its ability to detect cancer that has spread to the lymph nodes. PSMA is a protein that is usually found on the surface of normal prostate cells but is found in higher amounts on prostate tumor cells. Studies have shown that expression of PSMA is regulated by androgens (male reproductive hormones). Relugolix binds to gonadotropin-releasing hormone receptors in the pituitary gland, which blocks the pituitary gland from making the hormones follicle-stimulating hormone and luteinizing hormone. This causes the testicles to stop making testosterone. Relugolix may stop the growth of tumor cells that need testosterone to grow. PSMA PET/CT is an imaging procedure that is used to help find prostate tumor cells in the body. For this procedure, a cell-targeting molecule linked to a radioactive substance (flotufolastat F 18 in this trial) is injected into the body and travels through the blood. It attaches to PSMA that is found on the surface of prostate tumor cells. PET/CT scanners detect high concentrations of the radioactive molecule and shows where the prostate tumor cells are in the body. Giving a short course of ADT with relugolix may increase PSMA expression to detect smaller areas of prostate cancer that were not previously detected.

PRIMARY OBJECTIVE:

I. Comparison of maximum standard uptake value (SUVmax) and SUVmean values of the dominate primary prostate lesion between pre and post androgen deprivation therapy (ADT) imaging using flotufolastat F-18 gallium (POSLUMA [flotufolastat F 18]) PET/CT.

SECONDARY OBJECTIVES:

I. Evaluate and compare the lymph node sensitivity between pre and post ADT imaging using POSLUMA (flotufolastat F 18) PET/CT.

II. Comparison of lymph node prostate-specific membrane antigen (PSMA) avidity between pre and post ADT imaging using POSLUMA (flotufolastat F 18) PET/CT.

OUTLINE: Patients are randomized to 1 of 3 arms.

ARM A: Patients receive flotufolastat F 18 and undergo PET/CT on day 0. Patients then receive relugolix orally (PO) once daily (QD) on days 1-5 in the absence of disease progression or unacceptable toxicity. Patients also receive flotufolastat F 18 and undergo PET/CT on day 5. Patients then undergo robotic radical prostatectomy with pelvic lymph node dissection within 90 days of 2nd flotufolastat F 18 PET/CT scan. In addition, patients undergo collection of blood samples throughout the study.

ARM B: Patients receive flotufolastat F 18 and undergo PET/CT on day 0. Patients then receive relugolix PO QD on days 1-10 in the absence of disease progression or unacceptable toxicity. Patients also receive flotufolastat F 18 and undergo PET/CT on day 10. Patients then undergo robotic radical prostatectomy with pelvic lymph node dissection within 90 days of 2nd flotufolastat F 18 PET/CT scan. In addition, patients undergo collection of blood samples throughout the study.

ARM C: Patients receive flotufolastat F 18 and undergo PET/CT on day 0. Patients then receive relugolix PO QD on days 1-15 in the absence of disease progression or unacceptable toxicity. Patients also receive flotufolastat F 18 and undergo PET/CT on day 15. Patients then undergo robotic radical prostatectomy with pelvic lymph node dissection within 90 days of 2nd flotufolastat F 18 PET/CT scan. In addition, patients undergo collection of blood samples throughout the study.

Inclusion Criteria:

• Age ≥ 18 years

• Histological confirmation of prostate adenocarcinoma

• Diagnosis of high risk or very high risk prostate cancer per National Comprehensive Cancer Network (NCCN) Risk Stratification. [Any of the following: grade group 4 or 5, prostate-specific antigen (PSA) greater than 20, radiographic cT3 on MRI]

• Testosterone greater than or equal to 300

• Eastern Cooperative Oncology Group (ECOG) performance status (PS) 0, 1 or 2

• Hemoglobin ≥ 9.0 g/dL (obtained ≤ 120 days prior to registration/randomization)

• Absolute neutrophil count (ANC) ≥ 1500/mm^3 (obtained ≤ 120 days prior to registration/randomization)

• Platelet count ≥ 100,000/mm^3 (obtained ≤ 120 days prior to registration/randomization)

• Male patients who are committed to undertaking the following measures for the duration of the study and after the last dose of ORGOVYX (relugolix) for the time period specified:

  • Use a condom during sex while being treated and for 30 days after the last dose of ORGOVYX (relugolix)

  • Do not make semen donations during treatment and for 30 days after the last dose of ORGOVYX (relugolix)

  • Those with female partners of childbearing potential may be enrolled if they are:

    • Documented to be surgically sterile (i.e., vasectomy);
    • Committed to practicing true abstinence during treatment and for 30 days after the last ORGOVYX (relugolix) dose; or
    • Committed to using an effective method of contraception with their partner during treatment and for 30 days following the last dose of ORGOVYX (relugolix)

• Provide written informed consent

Exclusion Criteria:

• Any of the following prior therapies:

  • Chemotherapy ≤ 2 weeks prior to registration/randomization
  • Androgen deprivation therapy
  • Pelvic radiation

• Co-morbid systemic illnesses or other severe concurrent disease which, in the judgment of the investigator, would make the patient inappropriate for entry into this study or interfere significantly with the proper assessment of safety and toxicity of the prescribed regimens

• Uncontrolled intercurrent illness including, but not limited to:

  • Ongoing or active infection
  • Symptomatic congestive heart failure
  • Unstable angina pectoris
  • Cardiac arrhythmia
  • Or psychiatric illness/social situations that would limit compliance with study requirements

• Receiving any other investigational agent which would be considered as a treatment for the primary neoplasm

• Other active malignancy ≤ 1 year prior to registration

  • EXCEPTIONS: Non-melanotic skin cancer
  • NOTE: If there is a history of prior malignancy, they must not be receiving other active treatment for their cancer

• History of myocardial infarction ≤ 6 months, or congestive heart failure requiring use of ongoing maintenance therapy for life-threatening ventricular arrhythmias

• Use of P-glycoprotein inhibitors