This is a Phase II/III study. Patient population is adult participants with PSMA-positive mCRPC who had treatments with androgen receptor pathway inhibitor (ARPI) and taxane-based chemotherapy and progressed on or after \[177Lu\]Lu-PSMA targeted therapy. Treatment of interest: the investigational treatment is AAA817 regardless of subsequent anti-neoplastic treatment. The control treatment is investigator's choice of Standard of Care, regardless of subsequent anti-neoplastic treatment