Inclusion Criteria:

* Metastatic castration resistant prostate cancer (mCRPC) with histologic confirmation of adenocarcinoma (adenocarcinoma with small-cell or neuroendocrine features is allowed) with prior exposure to at least one androgen receptor (AR) targeted therapy (example, abiraterone acetate, enzalutamide, apalutamide, darolutamide). In addition: Part 1: prior taxane or other chemotherapy is acceptable but not required. Part 2a: prior taxane or other chemotherapy required, Part 2b: no prior taxane or other chemotherapy, Part 2c: mCRPC that has progressed after prior treatment with lutetium Lu-177 vipivotide tetraxetan
* Prior orchiectomy or medical castration; or, for 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
* Palliative radiotherapy (for example [eg], soft tissue lesions) must be completed greater than (>) 2 weeks prior to start of study drug except for palliative radiotherapy for pain (eg, bone pain), which may be used any time prior to first dose
* Eastern Cooperative Oncology Group (ECOG) performance status of 0 or 1
* Adequate organ functions as reflected in laboratory parameters

Exclusion Criteria:

* Prior treatment with radium Xofigo (Ra 223 dichloride), strontium, samarium, or other radioconjugate therapy. In addition: Part 2b: Prior treatment with chemotherapy (eg, docetaxel) or poly ADP ribose polymerase (PARP) inhibitors. Part 2c: Prior treatment with lutetium Lu-177 vipivotide tetraxetan is permitted
* Known history of myelodysplastic syndrome, leukemia, or hematological malignancy with features suggestive of myelodysplastic syndrome/acute myeloid leukemia at any timepoint
* Toxicity from prior anticancer therapy has not resolved to baseline levels or to Grade less than or equal to (<=) 1 (except alopecia, radiation tissue fibrosis, or peripheral neuropathy)
* Known allergies, hypersensitivity, or intolerance to JNJ-69086420 or its excipients and protein therapeutics
* Active or chronic hepatitis B or hepatitis C infection