Cabazitaxel +/- Carboplatin vs 177Lu-PSMA-617 in Metastatic Castrate-resistant Prostate Cancer

This study compares two treatment options for men with advanced prostate cancer that has stopped responding to hormone therapy (metastatic castrate-resistant prostate cancer). It compares a chemotherapy combination (cabazitaxel with or without carboplatin) against a radioactive drug treatment (lutetium-177 PSMA, which targets prostate cancer cells directly). **You may be eligible if...** - You have been diagnosed with metastatic castrate-resistant prostate cancer - Your cancer has previously been treated with a hormone therapy drug (androgen receptor pathway inhibitor) - A specialized scan (PSMA-PET) shows your cancer strongly expresses the PSMA protein - Your cancer is progressing despite current treatment **You may NOT be eligible if...** - Your PSMA scan does not show sufficient PSMA expression - You have not previously received androgen receptor pathway inhibitor therapy - Your overall health status does not meet the study's requirements Talk to your doctor to see if this trial is right for you.