The purpose of this study is to identify the recommended phase 2 combination dose (RP2CD) of JNJ-78278343 in combination with JNJ-95298177 in Part 1 (Dose confirmation) of the study and to determine how safe and tolerable the RP2CD is for treatment of participants with metastatic castration-resistant prostate cancer (mCRPC; a stage of prostate cancer where the cancer has spread beyond the prostate and is resistant to hormonal therapy) in Part 2 (Dose expansion) of study.
Histologically confirmed adenocarcinoma of the prostate. Primary small cell carcinoma, carcinoid tumor, neuroendocrine (NE) carcinoma, or large cell NE carcinoma arising in the prostate are not allowed; however, adenocarcinomas with NE features (for example [e.g.], immunohistochemistry [IHC] with both androgen receptor [AR]- and NE-marker positivity) are allowed
Must have metastatic castration-resistant prostate cancer (mCRPC)
PSA must measure at least 2 nanograms per milliliters (ng/mL) at screening
Measurable or evaluable disease
Toxicity related to prior anticancer therapy that has not returned to grade less than or equal to (<=) 1 or baseline levels (except for alopecia and vitiligo)
Known allergies, hypersensitivity, or intolerance to any of the components (e.g., excipients) of JNJ-78278343 or JNJ-95298177
Participants with leptomeningeal disease or brain metastases, with the exception of participants with definitively, locally treated brain metastases that are clinically stable and asymptomatic greater than (>) 2 weeks, and who are off corticosteroid treatment for at least 2 weeks prior to first dose of study treatment
Any T-cell redirecting treatment (e.g., CD3-directed bispecific or Chimeric Antigen Receptor T-cell [CAR-T] therapy) within 90 days prior to the first dose of study treatment