Study CAAA817A12201 consists of 2 parts: a randomized, open-label, international, multicenter, phase II study (Phase II) to collect more information to support the proposed dose of AAA817 and a randomized, open-label, international, multicenter, 2- arm phase III study (Phase III) aimed to evaluate the efficacy and safety of proposed dose of AAA817 vs. investigator's choice of standard of care (SoC) in the treatment of adult participants with PSMA-positive metastatic castration-resistant prostate cancer (mCRPC) who had treatments with ARPI and taxane-based chemotherapy, and progressed on or after [177Lu]Lu-PSMA targeted therapy. The purpose of the phase II part (Phase II) of this study is to collect additional information to support proposed phase III dose of AAA817.