Standard Systemic Therapy With or Without Definitive Treatment in Treating Participants With Metastatic Prostate Cancer

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.