A Study of JNJ-78278343 in Combination With Either JNJ-63723283 (Cetrelimab), Taxane Chemotherapy, or Androgen Receptor Pathway Inhibitors for Metastatic Prostate Cancer

Eligibility Criteria

Inclusion Criteria:

* Part 1 A-G (all combination treatments) and Parts 2B-C (cabazitaxel, docetaxel): Metastatic castration-resistant prostate cancer (mCRPC) with confirmed adenocarcinoma of the prostate as defined by prostate cancer working group 3 (PCWG3); Parts 2D-G (apalutamide, enzalutamide, darolutamide, abiraterone acetate + prednisone [AAP]): mCRPC: Histologically confirmed adenocarcinoma of the prostate as defined by PCWG3, with a minimum PSA of 2 nanogram [ng]/milliliter (mL); Part 2H (apalutamide): (a) metastatic hormone-sensitive prostate cancer(mHSPC) with non-castrate levels of testosterone (greater than [>] 150 ng/ deciliter [dL]) and a minimum PSA of 2 ng/milliliter [mL]; (b) Metastatic disease documented by greater than equal to (>=) 1 bone lesion(s) on technetium-99m (99m^Tc) bone scan. No definitive evidence of metastatic visceral disease
* Measurable or evaluable disease
* (a) Part 1A (cetrelimab) - Prior treatment for mCRPC with at least 1 prior androgen receptor pathway inhibitors (ARPI) (that is, abiraterone acetate, apalutamide, enzalutamide, darolutamide), or chemotherapy (example, docetaxel). (b) Part 1C and 2C (docetaxel), Part 1D (apalutamide), Part 1E and 2E (enzalutamide), Part 1F and 2F (darolutamide), and Part 1G and 2G (AAP)- Prior treatment with at least 1 prior ARPI (that is, apalutamide, enzalutamide, darolutamide, or abiraterone acetate). (C) Part 1B and 2B (cabazitaxel) - Prior treatment with at least 1 prior ARPI (ie, abiraterone acetate, apalutamide, enzalutamide, darolutamide) and docetaxel. (d) Part 2D (apalutamide) - Prior treatment with at least 1 prior ARPI (e) Part 2H (apalutamide)- Participant must not have received prior cytotoxic chemotherapy
* 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 and 2B , docetaxel Part 1C and 2C , apalutamide (Part 1D and 2D and Part 2H), enzalutamide (Part 1E and 2E), darolutamide (Part 1F and 2F), or AAP (Part 1G and 2G)
* Significant infections or serious lung, heart or other medical conditions