Combining radiation therapy with hormone treatments for advanced prostate cancer

Inclusion Criteria:

* Age ≥ 18 years
* Disease characteristics:

  * DEVIATE (Groups A and B only):

    * Clinical confirmation of metachronous (metastatic) recurrent hormone-sensitive prostate cancer
    * Five (5) or fewer metastases with at least one metastasis beyond the pelvis on advanced molecular and/or conventional imaging
    * Serum testosterone \> 100ng/dL or clinically deemed non-castrate
  * BRIO (Groups C \& D only):

    * Prostate-specific antigen (PSA) between 0.15 and 1.5 ng/mL with PSA ≥ 0.15 ng/mL on at least two measurements at least 5 days apart
    * No local or metastatic recurrence apparent on advanced molecular imaging
    * Serum testosterone \> 100 ng/dL or clinically deemed non-castrate
* Eastern Cooperative Oncology Group (ECOG) Performance Status (PS) 0, 1 or 2
* Hemoglobin ≥ 8.0 g/dL (obtained ≤ 15 days prior to registration)
* Absolute neutrophil count (ANC) ≥ 1500/mm\^3 (obtained ≤ 15 days prior to registration)
* Platelet count ≥ 80,000/mm\^3 (obtained ≤ 15 days prior to registration)
* Alanine aminotransferase (ALT) or aspartate transaminase (AST) ≤ 3 x upper limit of normal (ULN) (≤ 5 x ULN for patients with liver involvement) (obtained ≤ 15 days prior to registration)
* Calculated creatinine clearance ≥ 30 ml/min using the Cockcroft-Gault formula (obtained ≤ 15 days prior to registration)
* Provide written informed consent
* Ability to complete questionnaire(s) by themselves or with assistance
* Willingness to provide mandatory blood specimens for correlative research
* Willingness to allow access to provide tissue specimens for correlative research
* Willing to return to enrolling institution for follow-up (during the active monitoring phase of the study)

Exclusion Criteria:

* Any of the following because this study involves an investigational agent, the genotoxic, mutagenic, and teratogenic effects of which on the developing fetus and newborn are unknown

  * Pregnant persons
  * Nursing persons
  * Persons of childbearing potential or able to father a child who are unwilling to employ adequate contraception
* Prior metastasis-directed therapy
* Any of the following prior therapies:

  * Surgery ≤ 3 weeks prior to registration
  * Chemotherapy for prostate cancer at any time
  * Androgen receptor pathway inhibitors such as abiraterone, apalutamide, darolutamide, or enzalutamide in the last 2 years
* Uncontrolled intercurrent non-cardiac illness including, but not limited to:

  * Ongoing or active infection
  * Psychiatric illness/social situations
  * Dyspnea at rest due to complications of advanced malignancy or other disease that requires continuous oxygen therapy
  * Any other conditions that would limit compliance with study requirements
* Receiving any other investigational agent which would be considered as a treatment for prostate cancer.
* Failure to recover from acute, reversible effects of prior therapy regardless of interval since last treatment EXCEPTION: Grade 1 peripheral (sensory) neuropathy that has been stable for at least 3 months since completion of prior treatment
* Co-morbid systemic illnesses or other severe concurrent disease which, in the judgment of the investigator, would make the patient inappropriate for entry into this study or interfere significantly with the proper assessment of safety and toxicity of the prescribed regimens
* Uncontrolled intercurrent illness including, but not limited to:

  * Ongoing or active infection
  * Symptomatic congestive heart failure
  * Unstable angina pectoris
  * Cardiac arrhythmia
  * Or psychiatric illness/social situations that would limit compliance with study requirements
* Receiving any other investigational agent which would be considered as a treatment for the primary neoplasm
* Other active malignancy ≤ 3 years prior to registration

  * EXCEPTIONS: Curatively treated non-melanotic skin cancer or papillary thyroid cancer
  * NOTE: If there is a history of prior malignancy, they must not be receiving other specific treatment such as chemotherapy or antihormonal therapy for their cancer
* History of myocardial infarction ≤ 6 months prior to registration, or congestive heart failure requiring use of ongoing maintenance therapy for life-threatening ventricular arrhythmias