The purpose of this study is to see whether the combination of a chemotherapy drug, carboplatin, along with the radioligand treatment, 177Lu-PSMA-617, is safe in treating prostate cancer and whether the combination is effective in shrinking or preventing growth of prostate cancer. The names of the study drugs used in this research study are: * Carboplatin (A type of chemotherapy) * 177Lu-PSMA-617 (A type of radioligand therapy)
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Maximum tolerated dose (MTD) or the Recommended Phase 2 dose (RP2D) of carboplatin administered in combination with 177Lu-PSMA-617
Timeframe: First 6 weeks of treatment