Randomized Phase II Trial of Targeted Radiation With no Castration for Mcrpc

Inclusion Criteria: * Subject must be 18 years of age or older at the time the Informed Consent is signed * The subject (or legally acceptable representative if applicable) must provide written informed consent for the trial * Pathologic diagnosis of prostate cancer of adenocarcinoma histology; presence small cell/neuroendocrine carcinoma is exclusionary * Metastatic disease as documented by: * Osseous metastases detected by technetium-99m (99mTc) planar bone scan or NaF PET scan, or CT scan at some point in patient's history * Soft tissue metastases documented on CT or MRI * PSMA avid metastatic disease as determined by 18F-DCFPyL: at least one lesion with PSMA avidity greater than that of liver (see Prescribing Information for Pluvicto) * Progressive castration resistant prostate cancer as defined by serum testosterone \< 50 ng/mL and one of the following: * PSA progression confirmed per Prostate Cancer Clinical Trials Working Group (PCWG3) * Radiographic progression of soft tissues according to Response Evaluation Criteria in Solid Tumors, version 1.1 (RECIST 1.1) modified based on PCWG3, or radiographic progression of bone according to PCWG3 * Prior use of a novel AR signaling inhibitor for 4 weeks, including abiraterone acetate plus prednisone/prednisolone, enzalutamide, apalutamide, and/or darolutamide NOTE: These AR signaling inhibitors may have been used for mCSPC, M0CRPC, and/or mCRPC. * ECOG PS grade of 0-2 * 10 metastases detectable on molecular imaging (PSMA and FDG PET) and amenable to SBRT * 20% of metastases that are FDG avid but PSMA negative * Metastases that are not detectable on PSMA and FDG PET do not count toward the total number of metastases, as they are presumed to represent adequately treated sites of disease * Life expectancy 6 months * Adequate organ function: * Hemoglobin (hgb) \> 8.0 g/dL * Absolute neutrophil count (ANC) \> 1500/ µL * Platelets \> 75,000/ µL * Total bilirubin 1.5 x ULN OR direct bilirubin ULN for participants with total bilirubin levels \>1.5 x ULN * ALT and AST 3.0 x ULN ( 5 x ULN for participants with liver metastases) (Child-Pugh class A and B allowed; Child-Pugh class C is excluded) * Creatinine \< (2.0 mg/dL) during screening evaluation (\>2.0 is allowed if EGFR \>30 mL/min/1.73 m2) * Subject must agree to use contraception during the treatment period plus an additional 120 days after the last dose of study treatment and must refrain from donating sperm during this period Exclusion Criteria: * Visceral metastases including liver and brain (lung metastases are allowed) * Small cell/neuroendocrine carcinoma by hematoxylin and eosin light histology (immunohistochemical detection of rare/occasional cells that stain for neuroendocrine markers such as synaptophysin, neuron specific enolase, or chromogranin A is not sufficient to make a diagnosis of small cell/neuroendocrine carcinoma) * Anti-neoplastic therapies for prostate cancer must be completed \> 2 weeks prior to Day 1 (initiation of first dose of PSMA RLT) * Investigational agents must have been completed \> 4 weeks of Day 1 Note: Participants must have recovered from all AEs due to previous therapies to Grade 1 or baseline * Participants with Grade 2 neuropathy may be eligible * Herbal and non-herbal products that may decrease PSA levels other than medical castration and megestrol (up to 40 mg/day is allowed) for hot flashes * Has received prior radiotherapy within 2 weeks of start of study treatment. Participants must have recovered from all radiation-related toxicities, not require corticosteroids, and not have had radiation pneumonitis Note: Participants who have entered the follow-up phase of an investigational study may participate as long as it has been 4 weeks after the last dose of the previous investigational agent. * If a subject has undergone major surgery, they must have recovered adequately from the toxicities or complications from the intervention within 4 weeks prior to starting therapy * History of non-prostate active malignancy requiring treatment in the 24 months prior to Day 1 except for non-muscle invasive urothelial cancer, non-melanoma skin cancer, or any cancer that in the opinion of the investigator has been adequately treated and will not interfere with study procedures or interpretation of results * Active infection or conditions requiring treatment with antibiotics * Symptomatic local recurrence in the setting of prior curative intent therapy (surgery and/or radiation to the prostate) * Has a history or current evidence of any condition, therapy, or laboratory abnormality that might confound the results of the study, interfere with the subject's participation for the full duration of the study, or is not in the best interest of the subject to participate, in the opinion of the treating investigator * Has known psychiatric or substance abuse disorders that would interfere with cooperation with the requirements of the trial * Subject is planning to conceive or father children within the projected duration of the study, starting with the screening visit through 120 days after the last dose of trial treatment * Current or impending cord compression or another indication for urgent palliative radiation therapy