Study Comparing AAA817+ARPI Versus Standard of Care in Adult Participants With PSMA-positive mCRPC

Key Inclusion Criteria: * Signed informed consent must be obtained prior to participation in the study. * Participants must be adults ≥ 18 years of age. * Participants must have an ECOG performance status of 0 to 2. * Participants must have histological, and/or cytological confirmation of adenocarcinoma of the prostate. Participants with mixed histology (neuroendocrine) are not eligible. * Participants who have received taxane-based chemotherapy in mHSPC setting are eligible if they are deemed appropriate for chemotherapy, ARPI change or AAA617 as the next line of therapy in the opinion of the Investigator. Note: Participants who have received taxane-based chemotherapy for mCRPC are excluded. * Participants must not have received taxane-based chemotherapy in mCRPC setting (allowed in mHSPC setting). * Participants must have PSMA-PET positive disease using a PSMA imaging agent that is approved as per protocol. * Participant must have been diagnosed with mCRPC with documented progressive disease while on treatment with ARPI in mHSPC or earlier setting as their last treatment (and did not progress on more than one ARPI). * Participants with deleterious or suspected deleterious germline or somatic homologous recombination repair (HRR) gene-mutated metastatic castration-resistant prostate cancer, as per local testing, may be enrolled if they had prior exposure to PARPi. Key Exclusion Criteria: * Previous anti-cancer treatment with any approved or investigational radiopharmaceuticals (for example, \[177Lu\]Lu-PSMA, \[177Lu\]-DOTA, or Radium- 223.) * Previous treatment with any external beam radiotherapy including hemi-body radiation within 6 weeks of randomization (within 2 weeks for radiotherapy of localized metastases). * Any prior PARP inhibitor or other systemic anticancer therapy administered for metastatic castration-resistant prostate cancer (mCRPC). Any other approved or investigational systemic therapy (including chemotherapy, immunotherapy, biologics, or monoclonal antibodies) is prohibited within 28 days or 5 half-lives (whichever is shorter) before randomization. Note: Prior ARPI administered in the mHSPC setting or earlier may continue until C1D1. Other protocol-defined inclusion/exclusion criteria may apply.