Apalutamide With or Without Stereotactic Body Radiation in Treating Castration-Resistant Prostate Cancer

Inclusion Criteria: * Histologically or cytologically confirmed adenocarcinoma of the prostate * Progressive, castration-resistant prostate cancer demonstrated during continuous antiandrogen therapy (ADT), defined as 3 PSA rises at least 1 week apart, with a minimum PSA \> .05 ng/mL obtained during screening. * At least one but no more than 5 discrete PSMA-avid radiation fields on baseline PSMA-PET scan; all PSMA-avid lesions in radiation fields must be amenable to SBRT in judgment of treating radiation oncologist; there are no restrictions on site of lesion/radiation fields (e.g. bone, lymph node, prostate, visceral). Equivocal lesions/radiation fields on PSMA PET scan that are not definitive for metastasis will not count towards the limit of 5 radiation fields and will not undergo SBRT * Surgically or medically castrated, with testosterone levels of \< 50 ng/dL during screening; if the patient is medically castrated, continuous dosing with luteinizing hormone-releasing hormone (LHRH) analogue must have been initiated at least 4 weeks prior to randomization and must be continued throughout the study to maintain castrate levels of testosterone including post-treatment follow up period * No prior systemic treatment initiated for the treatment of castration resistant prostate cancer, including abiraterone acetate, enzalutamide, apalutamide, darolutamide, other novel AR or CYP17 antagonist, or docetaxel. * Patients receiving bone loss prevention treatment with bone-modifying ag…