Erdafitinib for the Treatment of Patients With Castration-Resistant Prostate Cancer

Inclusion Criteria: * Age \>= 18 years * Histologically proven adenocarcinoma or small cell of the prostate with evidence for skeletal metastases on bone scan and/or computed tomography (CT)/positron emission tomography (PET)/magnetic resonance imaging (MRI) scan. Eastern Cooperative Oncology Group (ECOG) performance status =\< 2 * Serum testosterone levels =\< 50 ng/ml and maintenance of castration with luteinizing hormone-releasing hormone (LHRH) agonist/antagonist or orchiectomy * Patients must have documented evidence of progressive disease as defined by any of the following: * PSA progression: minimum of 2 rising values (3 measurements) obtained a minimum of 7 days apart with the last result being at least \>= 1.0 ng/mL * New or increasing non-bone disease (Response Evaluation Criteria in Solid Tumors \[RECIST\] 1.1 criteria) * Positive bone scan with 2 or more new lesions (Prostate Cancer Working Group 3 \[PCWG3\]) * Prior treatment with a second-generation AR-targeting agent (e.g. abiraterone acetate, enzalutamide, apalutamide) is required. Patients may have received up to two such agents * Patients may have received prior treatment with immunotherapies (sipuleucel-T, checkpoint immunotherapies) or bone targeting therapies (radium-223) * Both chemotherapy-naive and patients previously treated with chemotherapy are eligible. Chemotherapy pretreated patients may have received a maximum of two prior systemic cytotoxic chemotherapies completed at least 3 weeks prior to initiation of study treatment * Hemoglobin \>= 8.0 g/dL * Platelet count \>= 75,000/uL * Absolute neutrophil count (ANC) \>= 1,500/mm\^3 * Calculated creatinine clearance (Cockcroft-Gault Equation) \>= 40 mL/min * Serum potassium \>= institutional lower limit of normal (ILLN) * Serum magnesium \>= ILLN * Serum albumin \>= 3.0 g/dL * Serum bilirubin \< 1.5 x institutional upper limit of normal (IULN) (except for patients with known Gilbert's disease) * Serum aspartate aminotransferase (AST) or alanine aminotransferase (ALT) \< 2.5 x IULN for patients without liver metastases. For patients with liver metastases AST or ALT \< 5 x IULN is allowed * Able to swallow study drugs whole as a tablet/capsule * Patients must agree to tissue and blood collection for correlative studies at the specified time points * Male subject with a female partner of childbearing potential or pregnant must agree to use two acceptable methods of contraception and not to donate sperm from time of screening until 3 months after the last dose of study treatments Exclusion Criteria: * Radiation therapy to primary tumor or metastatic sites within 2 weeks of cycle 1, day 1 * Treatment with any other investigational agent or participation in another clinical study with therapeutic intent within 30 days prior to randomization * A malignancy (other than the one treated in this study) which required radiotherapy or systemic treatment within the past 1 year, or has a \>= 30% probability of recurrence within 24 months (except for non-melanoma skin cancer or Ta urothelial carcinomas) * Chronically uncontrolled hypertension, defined conventionally as consistent systolic pressures above 160 or diastolic pressures above 100 despite anti-hypertensive therapy. Note that this is NOT a criterion related to particular blood pressure (BP) results at the time of assessment for eligibility, nor does it apply to acute BP excursions that are related to iatrogenic causes, acute pain or other transient, reversible causes. (For example doctor's visit related stress i.e. "white coat syndrome") * Eye conditions likely to increase the risk of eye toxicity including * Corneal or retinal abnormality likely to increase the risk of eye toxicity, or lens conditions such as: untreated mature or hypermature senile cataract, affecting visual acuity that impair the ability to interpret the Amsler grid test * History of central serous retinopathy (CSR) or retinal vascular occlusion (RVO) * Active wet, age-related macular degeneration (AMD) * Diabetic retinopathy with macular edema (non-proliferative) * Uncontrolled glaucoma (per local standard of care) * Corneal pathology such as keratitis, keratoconjunctivitis, keratopathy, corneal abrasion, inflammation or ulceration * Any underlying medical or psychiatric condition, which in the opinion of the investigator, will make the administration of study drug hazardous or obscure the interpretation of adverse events * History of uncontrolled cardiovascular disease including: * Unstable angina, myocardial infarction, ventricular fibrillation, Torsades de Pointes, cardiac arrest, or known congestive heart failure class III-V within the preceding 3 months; cerebrovascular accident or transient ischemic attack within the preceding 3 months * Mobitz II second degree heart block or third degree heart block * Corrected QT interval (QTc) prolongation as confirmed by triplicate assessment at screening (Fridericia; QTc \> 480 milliseconds) * Pulmonary embolism or other venous thromboembolism (VTE) within the preceding 2 months * Known active autoimmune deficiency syndrome (AIDS) (human immunodeficiency virus \[HIV\] infection), unless the subject has been on a stable anti-retroviral therapy regimen for the last 6 months or more, has had no opportunistic infections in the last 6 months, and has CD4 count \> 350 * Known active hepatitis B or C infection (subjects with history of hepatitis C infection but negative hepatitis C virus polymerase chain reaction (\[PCR\] test and subjects with hepatitis B with positive hepatitis B surface antibody are allowed) * Not recovered from reversible toxicity of prior anticancer therapy (except toxicities which are not clinically significant such as alopecia, skin discoloration, grade 1 neuropathy, grade 1-2 hearing loss) * Impaired wound healing capacity defined as skin/decubitus ulcers, chronic leg ulcers, known gastric ulcers, or unhealed incisions * Major surgery within 4 weeks before randomization * Untreated symptomatic spinal cord compression