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

Inclusion Criteria: * Histologically 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 Exclusion Criteria: * Active autoimmune disease 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 informed consent: 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