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.

QUALITY OF LIFE OBJECTIVES:

I. To compare between arms patient-reported urinary function and urinary bother over time (after initiation of SST at 6 months, 1, 2, and 3 years) using the Expanded Prostate Cancer Index Composite (EPIC) and patient-reported pain and physical functioning using the European Organization for Research and Treatment of Cancer Quality of Life Questionnaire (EORTC QLQ-C30) between patients receiving standard systemic therapy and those receiving systemic therapy and definitive management of the primary prostate cancer.

OTHER OBJECTIVES:

I. To bank tissue and whole blood specimens for future use.

OUTLINE:

INDUCTION: Participants receive 1 of 6 acceptable forms of SST for 22-28 weeks. I. Participants undergo a bilateral orchiectomy. II. Participants receive goserelin acetate subcutaneously (SC) every 28 days or 12 weeks, histrelin acetate SC every 12 months, leuprolide acetate SC or intramuscularly (IM) every 1, 3, 4, or 6 months, and triptorelin every 1, 3, or 6 months.

III. Participants receive goserelin acetate SC every 28 days or 12 weeks, histrelin acetate SC every 12 months, leuprolide acetate SC or IM every 1, 3, 4, or 6 months, and triptorelin every 1, 3, or 6 months. Participants also receive nilutamide orally (PO) daily, flutamide PO every 8 hours, and bicalutamide PO daily.

IV. Participants receive degarelix via injection for 2 doses and then every 28 days.

V. Participants receive nilutamide PO daily, flutamide PO every 8 hours, and bicalutamide PO daily. Participants also receive docetaxel over 1 hour every 3 weeks with or without prednisone PO every 12 hours.

VI. Participants receive nilutamide PO daily, flutamide PO every 8 hours, and bicalutamide PO daily. Participants also receive abiraterone PO daily or prednisone PO every 12 hours.

After completion of 22-28 weeks of SST, participants are then randomized to 1 of 2 arms.

ARM I: Participants receive 1 acceptable form of SST as in Induction except for treatment with docetaxel and prednisone.

ARM II: Participants receive 1 acceptable form of SST as in Induction except for treatment with docetaxel and prednisone. Participants undergo prostatectomy within 8 weeks after randomization or radiation therapy within 4 weeks of randomization.

After completion of study treatment, participants are followed up for 8 years.

Inclusion Criteria:

• STEP 1 REGISTRATION: DISEASE-RELATED CRITERIA: All patients must have a histologically or cytologically proven diagnosis of adenocarcinoma of the prostate. Patients with pure small cell carcinoma* (SCC), sarcomatoid, or squamous cell carcinoma are not eligible. (*morphology must be consistent with SCC; synaptophysin or chromogranin positive by immunohistochemical staining is insufficient to diagnose SCC).
• STEP 1 REGISTRATION: DISEASE-RELATED CRITERIA: Patients must have an intact prostate. No prior local therapy for prostate adenocarcinoma is allowed (e.g., brachytherapy, high-intensity focused ultrasound [HIFU], cryotherapy, laser ablative therapies). Any prior therapy for benign conditions, such as obstruction, are acceptable (e.g., transurethral resection of the prostate, greenlight laser ablation, microwave ablation).
• STEP 1 REGISTRATION: DISEASE-RELATED CRITERIA: Patients must have evidence of metastatic disease on technetium bone scan and computed tomography (CT) or magnetic resonance imaging (MRI) within 42 days prior to starting standard systemic therapy. Metastatic disease that is detected by positron emission tomography (PET) scan only (sodium fluoride [NaF], prostate-specific membrane antigen [PSMA], anti-1-amino-3-18F-fluorocyclobutane-1-carboxylic acid [FACBC], carbon [C]11) but not conventional imaging (technetium [Tc]99 bone scan, CT or MRI) or solitary metastases by conventional imaging, must be confirmed histologically or cytologically.
• STEP 1 REGISTRATION: DISEASE-RELATED CRITERIA: Patients with known brain metastases are not eligible. Brain imaging studies are not required for eligibility if the patient has no neurologic signs or symptoms suggestive of brain metastasis. If brain imaging studies are performed, they must be negative for disease.
• STEP 1 REGISTRATION: PRIOR/CONCURRENT THERAPY CRITERIA: Patients must have received no more than 28 weeks of standard systemic therapy (SST). SST is defined as current National Comprehensive Cancer Network (NCCN) guidelines for metastatic prostate cancer.
• STEP 1 REGISTRATION: PRIOR/CONCURRENT THERAPY CRITERIA: Patients must not have progressed while on SST.
• STEP 1 REGISTRATION: PRIOR/CONCURRENT THERAPY CRITERIA: Patients with oligometastatic prostate cancer may receive metastasis directed therapy to up to four sites of disease prior to randomization.
• STEP 1 REGISTRATION: CLINICAL/LABORATORY CRITERIA: Patients must have a complete physical examination and medical history within 28 days prior to registration.
• STEP 1 REGISTRATION: CLINICAL/LABORATORY CRITERIA: Patients must have a PSA documented prior to initiation of SST and within 28 days prior to registration. Any additional PSAs measured while receiving SST should be recorded.
• STEP 1 REGISTRATION: CLINICAL/LABORATORY CRITERIA: Patients must have a testosterone lab documented within 28 days prior to randomization. Any additional testosterone labs measured while receiving SST should be recorded as well as pretreatment initiation if available.
• STEP 1 REGISTRATION: CLINICAL/LABORATORY CRITERIA: No other prior malignancy is allowed except for the following: adequately treated basal cell or squamous cell 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.
• STEP 1 REGISTRATION: SPECIMEN SUBMISSION CRITERIA: Patients must be offered the opportunity to participate in translational medicine studies and specimen banking for future studies.
• STEP 1 REGISTRATION: QUALITY OF LIFE CRITERIA: Patients who can complete Patient-Reported Outcome instruments in English, Spanish or French, must participate in the quality of life studies.
• STEP 1 REGISTRATION: REGULATORY CRITERIA: Patients must be informed of the investigational nature of this study and must sign and give written informed consent in accordance with institutional and federal guidelines.
• STEP 2 RANDOMIZATION: DISEASE-RELATED CRITERIA: As a part of the OPEN registration process the treating institution's identity is provided in order to ensure that the current (within 365 days) date of institutional review board approval for this study has been entered in the system.
• STEP 2 RANDOMIZATION: DISEASE-RELATED CRITERIA: Patients must have no evidence of disease progression during the 28 weeks of SST by PSA measure, bone scan and CT or MRI or symptomatic deterioration (as defined by physician discretion) within 28 days prior to randomization.
• STEP 2 RANDOMIZATION: DISEASE-RELATED CRITERIA: Patients must have consultation with a urologist and have surgically resectable disease regardless of definitive treatment intent or randomization.
• STEP 2 RANDOMIZATION: PRIOR/CONCURRENT THERAPY CRITERIA: Patients must have received between 22 and 28 weeks of SST as measured from the date of first hormonal therapy or surgical castration. SST is defined by current NCCN guidelines for metastatic prostate cancer.
• STEP 2 RANDOMIZATION: PRIOR/CONCURRENT THERAPY CRITERIA: Patients must not be planning to receive docetaxel after randomization.
• STEP 2 RANDOMIZATION: PRIOR/CONCURRENT THERAPY CRITERIA: Any toxicities from SST must have resolved to =< grade 1 (Common Terminology Criteria for Adverse Events [CTCAE] version 5.0) prior to randomization.
• STEP 2 RANDOMIZATION: PRIOR/CONCURRENT THERAPY CRITERIA: Patients may have received elective metastasis directed therapy to oligometastatic sites (=< 4 sites). All treatment must be completed prior to randomization.
• STEP 2 RANDOMIZATION: CLINICAL/LABORATORY CRITERIA: Patients must have a PSA performed within 28 days prior to randomization.
• STEP 2 RANDOMIZATION: CLINICAL/LABORATORY CRITERIA: Patients must have a testosterone < 50 ng/dL within 28 days prior to randomization.
• STEP 2 RANDOMIZATION: CLINICAL/LABORATORY CRITERIA: Patients must have a Zubrod performance status of 0 ? 1 within 28 days prior to randomization.