Veterans Affairs Seamless Phase II/III Randomized Trial of STAndard Systemic theRapy With or Without PET-directed Local Therapy for Oligometastatic pRosTate Cancer

Inclusion Criteria: * Ability to provide Informed Consent for participation in the study ECOG Performance Status 2 at time of enrollment. Prostate cancer, confirmed histologically or cytologically. If original documentation of histology and cytology are not available, documentation of prostate cancer satisfies these criteria. If recurrent, prior curative-intent local therapy to all sites of prostate cancer with either upfront radiotherapy or prostatectomy with or without post-operative radiotherapy * If recurrent, prostate-specific antigen (PSA) suspicious for biochemical recurrence after local therapy, with lab value(s) taken prior to start of standard systemic therapy (SST), if current standard systemic therapy has already started, or within 90 days prior to enrollment if not already on standard systemic therapy, and meeting one of the three below categories: * Prostate-specific antigen (PSA) 0.2 nanograms per milliliter (ng/ml) x 2 after prostatectomy +/- post-operative radiotherapy; Elevation of prostate-specific antigen 2 nanograms per deciliter (ng/dl) above the nadir after definitive radiotherapy; Or Two consecutively elevated PSAs with evidence of metastasis on the imaging studies * Serum testosterone obtained prior to randomization based on one of the criteria below: * For patients who have a history of a prior episode of therapy with standard systemic therapy agents for prostate cancer, a total testosterone 100 nanograms per deciliter (ng/dl) after completion of the prior episode of standard systemic therapy and before the start of current standard systemic therapy or within 30 days of starting current standard systemic therapy if the patient has already started standard systemic therapy for recurrence. * For patients who have no prior history of an episode of therapy with standard systemic therapy agents and have already started standard systemic therapy for recurrence, this pre-standard systemic therapy testosterone is not required. * Computed tomography (CT) or magnetic resonance imaging (MRI) abdomen/pelvis performed prior to start of standard systemic therapy (if current standard systemic therapy has already started) or within 90 days prior to enrollment if not already on standard systemic therapy. The results from the CT component of the PET/CT can be used to fulfill this criterion. This is optional for patients who have a PSMA PET/CTstandard systemic therapy Yechnetium (Tc99m-MDP) or sodium fluoride (NaF) bone scan (sodium fluoride preferred) performed prior to start of standard systemic therapy (if current standard systemic therapy has already started), or within 90 days prior to enrollment if not already on standard systemic therapy. This is optional for patients who have a PSMA PET/CT. Prostate PET/CT (currently PSMA, Fluciclovine, choline) performed prior to start of standard systemic therapy (if current standard systemic therapy has already started), or within 90 days prior to enrollment if not already on standard systemic therapy. * 1-10 lesions suspicious for nodal recurrence or metastasis from prostate cancer as determined by the investigator based on the above imaging studies * Has already undergone NPOP sequencing or a plan is in place for NPOP sequencing for prostate cancer For participants on standard systemic therapy at the time of enrollment only: * Has been on standard systemic therapy for 180 days. For participants with local recurrence after curative-intent local therapy on imaging: * Patients with local recurrence in the prostate, SV, or prostate bed are eligible as long as there is at least 1 nodal or distant metastatic recurrence * Biopsy must confirm local recurrence for patients who have had prior curative-intent radiation to the prostate, SV, or prostate bed * Candidate for salvage local therapy (refer to Section 10.4) as determined by a urologist or radiation oncologist (depending on the respective modality to be used to treat the local recurrence) For participants with de novo prostate cancer: -Candidate for prostate-directed radiation Exclusion Criteria: * Any current or prior evidence of castration-resistant prostate cancer, defined as two consecutive rises in serum prostate-specific antigen (PSA), obtained at a minimum of 1-week interval, with the final PSA value \>/= 1 nanograms per milliliter, while having a total testosterone \< 50 nanograms per deciliter) * Prior malignancy, except the following: * Adequately treated non-melanomatous skin cancer * Adequately treated Stage 0, I, or II cancer from which the patient is currently in complete remission; or * Any other cancer from which the patient has been disease free for three years * Presence of a symptomatic metastasis that requires palliative radiotherapy * Any known brain metastases, presence of leptomeningeal disease, malignant spinal cord compression, or malignant cauda equina syndrome * Prior nodal, bone, or visceral metastasis after curative-intent therapy other than those identified on the enrollment imaging studies which make the patient ineligible for PET-directed local therapy (per investigator discretion) * Prior radiation therapy to any sites requiring PET-directed local therapy or salvage local therapy that will lead to prohibitively high risk of toxicity from subsequent local therapy, as determined by the treating radiation oncologist (if radiation is intended as the study local therapy) or surgeon/urologist (if surgery is intended as the study local therapy) * Any other previous or current condition, which, in the judgement of the LSI, is likely to interfere with any STARPORT treatments or assessments