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

PRIMARY OBJECTIVE: I. To demonstrate whether the proportion of patients with an undetectable serum prostate specific antigen (PSA) at 6 months following cessation of apalutamide is higher with addition of stereotactic body radiation therapy (SBRT) to prostate specific membrane antigen (PSMA)-avid oligometastatic sites of disease compared to the group of patients receiving apalutamide monotherapy SECONDARY OBJECTIVES: I. To compare the time to PSA progression by Prostate Cancer Working Group (PCWG) criteria between treatment arms. II. To evaluate the safety and tolerability of apalutamide in combination with SBRT. EXPLORATORY OBJECTIVES: I. To characterize the metastatic pattern at baseline and at progression in these patients and to determine whether features of the baseline PSMA-PET scan are associated with treatment outcomes. OUTLINE: Participants are randomized to 1 of 2 arms. ARM A: Participants receive apalutamide PO QD on days 1-28. Courses repeat every 28 days for up to 52 weeks in the absence of disease progression or unacceptable toxicity. ARM B: Participants receive apalutamide orally (PO) once daily (QD) on days 1-28. Courses repeat every 28 days for up to 52 weeks in the absence of disease progression or unacceptable toxicity. Beginning 60 days after first dose of apalutamide, participants also undergo stereotactic body radiation therapy for 1-5 fractions. After completion of study treatment, participants are followed at for 30 days.