Inclusion Criteria:

          -  Histologic: metastatic castration-resistant prostate cancer (mCRPC) with histologic
             confirmation of adenocarcinoma. Adenocarcinoma with small-cell or neuroendocrine
             features is allowed

          -  Must have had prior exposure to at least one novel androgen receptor (AR) targeted
             therapy (example, abiraterone acetate, enzalutamide, apalutamide, darolutamide); prior
             taxane or other chemotherapy is acceptable but not required

          -  Treatment with other agents for prostate cancer, if received, must have been
             discontinued greater than or equal to (>=) 2 weeks prior to first dose of study drug.

          -  Eastern Cooperative Oncology Group (ECOG) performance status of 0 or 1

          -  Adequate organ functions as reflected in laboratory parameters

        Exclusion Criteria:

          -  Part 1: Prior treatment with radium Xofigo (Ra 223 dichloride), strontium, or samarium
             therapy or radioconjugate therapy

          -  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.