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This phase III trial studies how well standard systemic therapy with or without definitive treatment (prostate removal surgery or radiation therapy) works in treating participants with prostate cancer that has spread to other places in the body. Addition of prostate removal surgery or radiation therapy to standard systemic therapy for prostate cancer may lower the chance of the cancer growing or spreading.

PRIMARY OBJECTIVES: I. To compare overall survival in metastatic prostate cancer patients who are randomized to standard systemic therapy (SST) plus definitive treatment of the primary tumor versus standard systemic therapy alone. SECONDARY OBJECTIVES: I. To compare overall survival in metastatic prostate cancer patients who received SST plus surgical excision of the primary tumor versus SST alone in the subset who specify the surgical intent stratification factor. II. To compare the rate of symptomatic local progression between the treatment arms. III. To compare progression-free survival (PFS) between the two treatment arms. IV. To compare rates of progression-free survival between arms for the subsets of patients with and without metastasis directed therapy (MDT) to oligometastatic sites.