Salvage Oligometastasectomy and Radiation Therapy in Recurrent Prostate Cancer

Inclusion Criteria: * Histologically proven adenocarcinoma of the prostate. * Recurrent prostate carcinoma after definitive therapy for primary disease defined as: * Post-prostatectomy (with/without adjuvant radiotherapy): Patients must have a detectable or rising PSA level that is \> 0.05 ng/mL, with a second confirmatory level of \> 0.05 ng/mL after a minimum of 1 week. * Post radiotherapy/ablation (without radical prostatectomy): PSA rise \>= 2ng/mL over nadir. * Subjects treated with prior definitive radiotherapy for prostate cancer who have positive molecular imaging (e.g., fluciclovine PET/CT scan or other per PI discretion) suggesting recurrent intraprostatic disease must undergo transrectal ultrasound (TRUS) biopsy less than or equal to one year before study enrollment: * If the TRUS biopsy is negative, no additional treatment is required to the prostate in addition to that of scan positive sites. * If the TRUS biopsy is positive, subject must undergo salvage prostatectomy or salvage radiotherapy to the primary site concurrently with the study treatment per the treatment protocol algorithm. * NOTE: Biopsy is not required for prostate fossa recurrences after radical prostatectomy. * Oligometastatic disease defined as 10 or fewer metastatic lesions to lymph nodes and/or bones only. * For patients with oligometastatic disease involving lymph nodes, metastasis is confined to the pelvic or para-aortic (below IMA) regions on molecular imaging (e.g., fluciclovine PET/CT or PSMA PET/CT scan or other per PI discretion). * All subjects must be surgical candidates if surgery is indicated per the treatment algorithm. * Eastern Cooperative Oncology Group (ECOG) performance status =\< 2. * Use of condoms for male subjects who have not had surgical removal of their prostate and have a partner of child bearing potential beginning at the time of informed consent form (ICF) signature and lasting until at least 6 months after the last radiation treatment. Because of the potential side effect on spermatogenesis associated with radiation, female partners of childbearing potential must agree to use a highly effective contraceptive method during and for 6 months after completing treatment. * Recovery to baseline or =\< grade 1 Common Terminology Criteria for Adverse Events (CTCAE) version (v)5 from toxicities related to any prior treatments, unless adverse event (AE)(s) are clinically non-significant and/or stable on supportive therapy as determined by the treating physician. * Able to provide informed consent and willing to sign an approved consent form that conforms to federal and institutional guidelines. Exclusion Criteria: * Known brain or visceral metastases other than lymph nodes as defined by CT, MRI, or othermolecular imaging (e.g., fluciclovine PET/CT or PSMA PET/CT scan or other per PI discretion). * Patients actively receiving hormone therapy for prostate cancer. Patients may have received hormone therapy perviously but must have documented non-castrate levels of testosterone (\>50 ng/dL) * Prior or concurrent malignancy whose natural history or treatment, in the opinion of the enrolling investigator, may have the potential to interfere wih the safety or efficay assessment of the investigational treatment protocol of the study. * Use of finasteride within 30 days prior to initiation of therapy. Baseline PSA should not be obtained prior to 30 days after stopping finasteride. * Use of dutasteride within 90 days prior to initiation of therapy. Baseline PSA should not be obtained prior to 90 days after stopping dutasteride. * Use of any prohibited therapy. * Active, uncontrolled, significant intercurrent or recent illness including, but not limited to, the following conditions: * Cardiovascular disorders: * Congestive heart failure New York Heart Association class 3 or 4, unstable angina pectoris, serious cardiac arrhythmias. * Uncontrolled hypertension defined as sustained blood pressure (BP) \> 150 mmHg systolic or \> 100 mmHg diastolic despite optimal antihypertensive treatment. * Stroke (including transient ischemic attack \[TIA\]), myocardial infarction (MI), or other ischemic event, or thromboembolic event (e.g., deep venous thrombosis, pulmonary embolism) within 6 months before first dose. * Acute bacterial or fungal infection requiring intravenous antibiotics at the time of registration * Chronic obstructive pulmonary disease exacerbation or other respiratory illness requiring hospitalization or precluding study therapy at the time of registration or within 30 days of registration. * Hepatic insufficiency resulting in clinical jaundice and/or coagulation defects.