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

Inclusion Criteria: * Participants must have histologically or cytologically confirmed adenocarcinoma of prostate * Evidence of metastatic castrate-resistant prostate cancer that has previously been treated with an androgen receptor pathway inhibitor. Prior docetaxel exposure is recommended but not mandatory. Tissue is not mandatory, but a pathologic report is required at time of enrollment. * Patients must have a PSMA-positive 18F-rhPSMA-7.3 performed within 12 weeks from C1D1 with ≥1 site with SUVmax ≥10. An alternative PSMA PET tracer is permitted at baseline if performed within 8 weeks prior to randomization. * Eligible patients have evidence of mCRPC who have progressed on prior novel hormonal agent(s) to include at least one of the following: * Baseline PSMA SUVmean \<10 OR * ≥1 visceral metastasis OR * ≥5 bone metastases OR one of the following (using Next Generation Sequencing on file within 5 years) * TP53 * PTEN * mutation. * Age \> 18 years. * ECOG performance status of 0 to 2. * Participants must have adequate organ and marrow function as defined below to be suitable for the randomized treatment outlined in this * Absolute neutrophil count \>1000/μL; platelet count \>90 000/μL; hemoglobin \>8.5 g/dL) at screening. * Note: Participants must not have received any growth factors within 7 days or blood transfusions within 14 days prior to the hematologic laboratory values obtained at screening). * Total bilirubin (TBIL) \<2.5 × the upper limit of …