A Study of JNJ-87189401 Plus JNJ-78278343 for Advanced Prostate Cancer

Who May Qualify: - diagnosed by tissue sample (biopsy-confirmed) adenocarcinoma of the prostate. Adenocarcinoma with small cell or neuroendocrine (NE) features is permitted. However, small cell carcinoma, carcinoid tumor, mixed NE carcinoma, or large cell NE carcinoma is disallowed - Measurable or evaluable disease per PCWG3 criteria - Part 1, Part 2A and Part 2B: Prior orchiectomy or medical castration; participants who have not undergone orchiectomy, must be receiving ongoing androgen deprivation therapy with a gonadotropin releasing hormone (GnRH) analog (agonist or antagonist), prior to the first dose of study drug and must continue this therapy throughout the treatment phase - Have an Eastern Cooperative Oncology Group (ECOG) performance status of 0 or 1 Who Should NOT Join This Trial: - Active autoimmune conditions (where your immune system attacks your own body) within the 12 months prior to signing consent that requires systemic immunosuppressive medications (example, chronic corticosteroids, methotrexate, or tacrolimus) - Any of the following within 6 months prior to signature of willing to sign a consent form: a. myocardial infarction, b. severe or unstable angina, c. clinically significant ventricular arrhythmias, d. congestive heart failure (New York Heart Association \[NYHA\] class II to IV), e. transient ischemic attack, and f. Cerebrovascular accident Always talk to your doctor about whether this trial is right for you.