• Histologically confirmed prostate cancer prior to randomization

• Participants must have biochemically recurrent disease after definitive treatment to prostate by Radical Prostatectomy ((RP), (alone or with post-operative radiation to prostate bed/pelvic nodes)) or External beam Radiation Therapy (EBRT), (prostate alone or prostate with seminal vesicle and/or pelvic nodes) and/or brachytherapy prior to randomization. Biochemical recurrence (BCR) is defined as: nadir PSA + 2 ng/mL post XRT (if participant received-radiation therapy to intact prostate) and PSA \> 0.2 ng/mL and rising post RP (with or without post-operation Radiation Therapy (RT))

• Participants must have OMPC with 1-5 PSMA -positive metastatic lesions on screening PSMA PET/CT scan (with either gallium (68Ga) gozetotide or piflufolastat (18F)) as visually assessed by BIRC. For definition of PSMA PET positivity, please refer to Section 8.1 and the Imaging Manual. Metastatic lesions may include regional/pelvic lymph nodes (N1), distant lymph nodes (M1a), bone (M1b), lung and others visceral (M1c) except liver and brain classified using American Joint Committee on Cancer (AJCC) 8. When counting the number of oligometastatic lesions, each lesion is counted as distinct metastasis irrespective of its anatomical location (e.g., one pelvic and one extra-pelvic lymph node will be counted as two metastatic lesions)

• At least 1 PSMA-positive lesion must be a distant metastasis (M1) per AJCC8 classification at screening. For AJCC M staging, PSMA PET/CT information should be used

• Participants must have a negative CI for M1 disease at screening.

• Note:

⁃ For a participant not to be eligible, CI positive M1 lesions should be unequivocal in CI scans, i.e., potentially not attributable to findings thought to represent something other than tumor (e.g., degenerative, or post-traumatic changes or Paget's disease in bone lesions). For CI assessments, bone lesions must be assessed by bone scan only and soft tissue lesions must be assessed by CT/MRI scans only at screening.

⁃ Prior knowledge of PSMA PET positivity should not influence the radiologist (reader) in determination of CI positivity. Two different readers will be involved, one reader for PSMA PET/CT scan and one reader for CI: Reader will be blinded to PSMA PET scan results while reading CI scans. Reader should not modify their assessment of CI scans (e.g. changing a lesion previously identified as equivocal in CI to unequivocal) after reading the PSMA PET scan. Similarly, biopsy positivity should not influence the reader in the assessment of CI positivity. More details on the reading paradigm will be provided in the imaging charter

⁃ MRI for radiation treatment planning may show M1 disease but this will not exclude the participant from the study if the lesion is deemed negative per baseline CT or bone scans

⁃ Participants with pelvic disease (N1) seen in CI are allowed if the local spread is below common iliac bifurcation (per AJCC 8 definition of local disease)

⁃ Distant lymph node disease (M1a) that is visible per CI and less than 10mm in the short axis is not exclusionary irrespective of PSMA PET positivity.

⁃ If a previously surgically removed lesion was unequivocal for M1 by bone scan or CT, the participant is not eligible.

• All metastatic lesions detected at screening must be amenable to SBRT

• Non-castration testosterone level \>100 ng/dL at screening