Best Salvage Treatment for High-risk Relapsing Prostate Cancer (PEACE-9 - ESCALATE-RT)

The goal of this clinical trial is to learn if adding metastasis-directed radiotherapy with or without pelvic salvage radiotherapy, to intermittent prostate cancer drugs (intensified hormone therapy) can delay the need to restart these drugs in men with oligometastactic prostate cancer recurrence. In practice, this study is open to men whose PSA level (a blood marker of cancer activity) is rising as defined by biochemical recurrence, and who have 1 to 5 areas of cancer spread (1 to 5 metastases defining oligometastatic status) found on a specialized scan (PSMA PET/CT). Since intensified hormone therapy, including androgen deprivation therapy combined with a next-generation hormone therapy, represents the standard treatment strategy for these patients, researchers want to find out if adding radiation therapy can help patients to spend more time off cancer drugs while keeping their cancer under control. The main questions this trial aims to answer are: * Does adding radiation therapy to each metastases with or without pelvic area, lengthen the time before participants need to restart drug treatment? * Does adding radiation therapy increase the number of participants whose PSA drops to a very low level (0.2 ng/mL or lower)? * Does adding radiation therapy affect participants' quality of life? Researchers will randomly assign participants (chosen by chance) to receive either enzalutamide (next-generation hormone therapy) plus androgen-deprivation therapy (first-generation hormone therapy ) alone, or the same association of these drugs combined with radiation therapy aimed at each metastases with or without pelvic area. This comparison will show whether adding radiation therapy helps participants reach a deeper PSA response and go longer without needing cancer drugs. Participants will: * Take enzalutamide and androgen-deprivation therapy for 9 months * Have an equal chance of also receiving radiation therapy to each metastases with or without pelvic area * Stop d