This clinical trial is focused on studying a type of prostate cancer known as metastatic castration-resistant prostate cancer (mCRPC). This is a form of prostate cancer that continues to grow and spread even when the amount of testosterone in the body is reduced to very low levels. The study is comparing two different treatments for this condition. One treatment involves a medication called 177Lu-PSMA-617, which is a type of radiopharmaceutical. Radiopharmaceuticals are drugs that contain radioactive substances and are used to treat certain types of cancer. The other treatment involves changing the current therapy that targets androgen receptors, which are proteins in the body that respond to male hormones like testosterone.

The purpose of the study is to see if the treatment with 177Lu-PSMA-617 can help delay the progression of the cancer or extend the time before the cancer worsens, compared to the alternative therapy. Participants in the study will receive either the radiopharmaceutical treatment or a change in their current androgen receptor-directed therapy. The study will last for a period of time, during which participants will be monitored regularly to assess the effects of the treatment on their cancer.

In addition to the main treatments, the study will also involve the use of other medications such as abiraterone acetate and enzalutamide, which are commonly used in treating prostate cancer. These medications work by blocking the effects of male hormones that can promote the growth of cancer cells. The study aims to provide valuable information on the effectiveness of these treatments in managing metastatic castration-resistant prostate cancer.