Optimizing Treatment and Advanced Multi-Imaging Response Evaluation for Very-High-Risk Prostate Cancer (OPTIMAL) - a Phase II Single Arm Study

Inclusion Criteria: * Patients must have histologically confirmed prostate adenocarcinoma consistent with NCCN very-high-risk (VHR) prostate cancer defined with at least one of the following: * cT3b-cT4 (American Joint Committee on Cancer \[AJCC\] 9.0) * \> 4 cores with grade group 4 or 5 prostate cancer * Primary gleason pattern 5 * 2 or 3 NCCN high-risk features. * Patients with involved pelvic lymph nodes below the common iliac bifurcation will be allowed as long as the criteria for VHR (very-high risk) are met * Patients must be age ≥ 18 years * Patients must have testosterone \> 50 ng/dL within 90 days prior to registration * Note: Prior androgen deprivation (gonadotrophin releasing hormone \[GnRH\] analog and/or non-steroidal antiandrogen) therapy is allowed provided that it is less than 60 days of prior total duration and that serum testosterone concentration must be ≥ 50 ng/dL prior to enrollment; 5-alpha reductase inhibitors will not impact eligibility, but must be discontinued prior to starting protocol treatment * Patients must exhibit an Eastern Cooperative Oncology Group (ECOG) performance status of 0-2 * Leukocytes (white blood cells \[WBC\]) ≥ 2,500/mcL * Absolute neutrophil count (ANC) ≥ 1,500/mcL * Hemoglobin (Hgb) ≥ 8 g/dL * Platelets (PLT) ≥ 80,000/mcL * Aspartate aminotransferase (AST) (serum glutamic-oxaloacetic transaminase \[SGOT\]) ≤ 3 x institutional upper limit of normal (ULN) * Alanine aminotransferase (ALT) (serum glutamate pyruvate transaminase \[SGPT\]) ≤ 3 x institutional ULN * Creatinine ≤ institutional ULN * Glomerular filtration rate (GFR) ≥ 30 mL/min/1.73 m\^2 * Estimated GFR (eGFR) is estimated GFR calculated by the abbreviated Modification of Diet in Renal Disease (MDRD) equation * For patients with a known history of human immunodeficiency virus (HIV), infected patients on effective anti-retroviral therapy must have a viral load undetectable for 3 months prior to registration with a CD4 count of ≥ 200 cells/μL. Note also that HIV testing is not required for eligibility for this protocol as it is self-reported * Patients with known history or current symptoms of cardiac disease, or history of treatment with cardiotoxic agents, should have a clinical risk assessment of cardiac function using the New York Heart Association Functional Classification. To be eligible for this trial, patients should be better than class III * Patients must not have contraindications to magnetic resonance (MR) imaging and be able to lie flat and still for approximately 30-40 minutes and be able to tolerate PET/CT imaging and radiation therapy treatment planning and delivery * Patients with female partners of reproductive potential must agree to use effective contraception during treatment with and for 3 months after the last dose. Male patients must use a condom during sex with a pregnant woman * Patients must have the ability to understand and the willingness to sign a written informed consent document and comply with the study requirements Exclusion Criteria: * Patients with definitive clinical or radiologic evidence of metastatic disease * Patients with prior invasive malignancy (except non-melanomatous skin cancer carcinoma in situ of the male breast, penis, oral cavity, or stage Ta of the bladder, or stage I completely resected melanoma) unless disease free for a minimum of 2 years * Prior radiotherapy that would result in overlap of radiation therapy fields * Patients who have a history of any of the following: * History of documented inflammatory bowel disease * Symptomatic congestive heart failure (New York Heart Association Functional Classification III/IV) within 4 months prior to registration * Unstable angina pectoris requiring hospitalization within the last 4 months prior to registration * History of seizure disorder or condition that may yield a high risk of seizure (e.g., prior cortical stroke or significant brain trauma) * Psychiatric illness/social situations that would limit compliance with study requirements * History of repeated falls and fractures over the past 12 months that in the opinion of the treating investigator would put the patient at risk for poor bone outcomes from androgen receptor targeted therapy * Any other illness or condition that the treating investigator feels would interfere with study compliance or would compromise the patient's safety or study endpoints * Patients with the inability to take oral medication OR have malabsorption syndrome or any other uncontrolled gastrointestinal condition (eg, nausea, diarrhea, vomiting) that might impair the bioavailability of enzalutamide and relugolix