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.