Study of Recurrence-directed Therapy (RDT) With or Without Androgen-Deprivation Therapy (ADT) In Patients With Radio-recurrent Oligo-metastatic Hormone/Castrate Sensitive Prostate Cancer (romCSPC)

Inclusion Criteria: 1. Previous biopsy-proven localized prostate adenocarcinoma (without predominant features of sarcomatoid, small cell or neuroendocrine carcinoma) treated with definitive or salvage radiotherapy ≥ 2 years or more before enrollment. 2. Recurrent Oligo-metastatic CSPC, M0 on conventional imaging (bone scan and CT scan of chest/abdomen/pelvis) with ≤ 5 metastases cumulative on all imaging, including MRI and PSMA-PET. Note: Patients with conventional imaging M1 oligometastatic CSPC, who have no more than 5 metastatic sites in all imaging modalities including MRI and PSMA-PET, will be accepted for study enrollment. 3. All sites of recurrent disease must be amenable to treatment with radiotherapy or surgery in the judgment of the investigator. 4. Biochemical recurrent prostate cancer with ONE of the following PSA recurrence definitions: 1. After definitive radiotherapy (prostate in situ), with PSA ≥ nadir + 2ng/ml; 2. After prostatectomy and adjuvant/salvage radiotherapy, with PSA ≥ nadir + 0.2ng/ml. Exclusion Criteria: 1. Age \< 18. 2. ECOG Performance Status ≥3. 3. PSA ≥ 20 ng/ml. 4. Treatment with ADT within 2 years from study enrollment or treatment with any androgen receptor axis within 6 months from study enrollment. 5. Prior treatment with chemotherapy for prostate cancer or bilateral orchiectomy. Note: prior chemotherapy for a different type of cancer is allowed if the patient has been continuously disease-free for \> 3 years. 6. Intracranial or intrathecal metastasis. 7. Spinal cord compression, or spinal intramedullary metastasis. 8. Prior malignancy (except non metastatic, non- melanomatous skin cancer) unless disease free for \> 3 years. 9. Bilateral hip prosthesis, treated earlier with definitive prostate radiotherapy, who have evidence of local disease recurrence within the prostate and no option for salvage treatment with brachytherapy or surgery. 10. Previous documented hypersensitivity to ELIGARD® or other GnRH agonist analogs of components of such preparations.