Neratinib in Patients With Metastatic Castration-Resistant Prostate Cancer

Inclusion Criteria: * Histologically or cytologically confirmed metastatic prostate adenocarcinoma (secondary components of variant histology are acceptable). * Castration-resistance, with progression on medical/surgical castration and confirmed baseline testosterone \<50ng/dL * Ongoing castration, either with prior orchiectomy or ongoing gonadotropin releasing hormone (GnRH) agonist/antagonist therapy as per investigator discretion * Anti-resorptive therapy (e.g. denosumab, bisphosphonates) is allowable at any point * Prior progression on (or intolerance of) at least one androgen-receptor signaling inhibitor(i.e. abiraterone, enzalutamide, apalutamide, darolutamide). Progression is per investigator and can include prostate specific antigen (PSA), symptomatic, and/or radiographic progression. There is no limit to prior therapies, nor any requirement on taxane treatments. * Positive biomarker (phospho human epidermal growth factor receptor 2, pHER2) assessment on baseline tissue. Archival tissue is acceptable but must have been acquired during or after prior abiraterone and/or enzalutamide therapy and must meet tissue specifications outlined in the biomarker assessment section of the protocol. If suitable archival tissue is not available, then the patient must be willing to undergo a research biopsy to obtain tissue for biomarker assessment. * Evaluable for response, defined as at least one of the following: * Baseline PSA \>=2.0 ng/mL * Measurable disease per Response Evaluation Criteria in Solid Tumors (RECIST) 1.1 * Ability to understand and willingness to sign informed consent. * Willingness to undergo research biopsy on study, as well as at baseline if needed to obtain tissue for biomarker assessment. * Age \>=18 years * Eastern Cooperative Oncology Group (ECOG) performance status ≤2 * Adequate organ and marrow function as defined below: * leukocytes ≥2,000/mcL * absolute neutrophil count ≥1,500/mcL * platelets ≥100,000/mcL * total bilirubin ≤ 1.5 x institutional upper limit of normal (ULN), unless participant has known or suspected Gilbert's syndrome * AST(SGOT)/ALT(SGPT) ≤2.5 × institutional ULN or \<=5 x ULN if liver metastases present * Estimated glomerular filtration rate (eGFR) ≥ 30 mL/min * Male participants must agree to use contraception with any female partners who are of reproductive potential prior to the study entry, for the duration of the study participation, and 6 months after completion of administration. * Human immunodeficiency virus (HIV)-infected participants on effective anti-retroviral therapy with undetectable viral load within 6 months are eligible for this trial. * For participants with evidence of chronic hepatitis B virus (HBV) infection, the HBV viral load must be undetectable on suppressive therapy, if indicated. * Participants with a history of hepatitis C virus (HCV) infection must have been treated and cured. For participants with HCV infection who are currently on treatment, they are eligible if they have an undetectable HCV viral load. * Participants with brain metastases are eligible if (1) brain metastases are asymptomatic and patients are on a stable dose of corticosteroids (if needed) for 14 days prior to enrollment, or (2) brain metastases have been treated with local therapy and follow-up brain imaging shows no evidence of progression. * Participants with a prior or concurrent malignancy whose natural history or treatment does not have the potential to interfere with the safety or efficacy assessment of the investigational regimen are eligible for this trial. * Participants must be able to swallow pills. Exclusion Criteria: * Use of a strong CYP3A4/CYP2C8 inducer/inhibitor within 3 half-lives prior to first dose of study treatment * Participants who are receiving any other investigational agents * History of allergic reaction to HER2 inhibitors * Child-Pugh class C hepatic impairment * Current use of a proton pump inhibitor (no specific wash-out period) * Corrected QTc interval \>450 msec with institutional standard correction formula. One EKG is sufficient. In the case of potentially reversible causes of QT prolongation (e.g. medications, electrolyte abnormalities), EKG may be repeated once during screening and that result may be used to determine eligibility. * 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. * Uncontrolled baseline diarrhea or uncontrolled predisposition to intermittent diarrhea, e.g. uncontrolled inflammatory bowel diseases.