Inclusion Criteria:

* Metastatic castration-resistant prostate cancer (mCRPC) with confirmed adenocarcinoma of the prostate as defined by Prostate Cancer Working Group 3 (PCWG3)
* Measurable or evaluable disease.
* (a) Part 1A: JNJ-78278343 + cetrelimab - Prior treatment for mCRPC with at least 1 prior androgen receptor pathway inhibitors (ARPI) (that is, abiraterone acetate, apalutamide, enzalutamide, darolutamide), or chemotherapy (eg, docetaxel). (b) Part 1C: JNJ-78278343 + docetaxel, Part 1D: JNJ-78278343 + apalutamide, Part 1E: JNJ-78278343 + enzalutamide, Part 1F: JNJ-78278343 + darolutamide, and Part 1G: JNJ-78278343 + abiraterone acetate + prednisone - Prior treatment with at least 1 prior ARPI (that is, apalutamide, enzalutamide, darolutamide, or abiraterone acetate,). (C) Part 1B: JNJ-78278343 + cabazitaxel - Prior treatment with at least 1 prior ARPI (ie, abiraterone acetate, apalutamide, enzalutamide, darolutamide) and docetaxel.
* Eastern Cooperative Oncology Group (ECOG) performance status of 0 or 1
* Adequate organ functions

Exclusion Criteria:

* Active autoimmune disease within the 12 months prior to signing consent that requires systemic immunosuppressive medications
* Toxicity related to prior anticancer therapy that has not returned to Grade less than or equal to (<=) 1 or baseline levels (except for alopecia, vitiligo, Grade <=2 peripheral neuropathy)
* Solid organ or bone marrow transplantation
* Known allergies, or intolerance to any of the components (example, excipients) of JNJ-78278343, cetrelimab (Part 1A), cabazitaxel, (Part 1B), docetaxel (Part 1C), apalutamide (Part 1D), enzalutamide (Part 1E), darolutamide (Part 1F), or abiraterone acetate + prednisone (AAP) (Part 1G)
* Significant infections or serious lung, heart or other medical conditions