An Open-label Study of Lutetium (177Lu) Vipivotide Tetraxetan (AAA617) in Combination With ARPI Versus AAA617 in PSMA Positive First-line mCRPC

Key Inclusion Criteria: * Participants must have an ECOG performance status of 0 to 2. * Participants must have histopathological, and/or cytological confirmation of adenocarcinoma of the prostate. * Participants must have PSMA PET positive disease using FDA approved PSMA-imaging approved agents, and eligible as determined by the sponsor's central reading rules. * Participants must have a castrate level of serum/plasma testosterone (\< 50 ng/dL or \< 1.7 nmol/L). * Newly diagnosed mCRPC participants who must have progression on prior ARPI in the BCR-non mHSPC, mHSPC, or nmCRPC setting. * Participants must have progressed only once on prior second-generation ARPI (abiraterone, enzalutamide, darolutamide, or apalutamide). First generation androgen receptor inhibitor therapy (e.g. bicalutamide) is allowed but not considered as prior ARPI therapy (second generation ARPI must be the most recent therapy received). * Participant must have been diagnosed with mCRPC with documented progressive disease after having been previously treated with ARPI in the BCR-non mHSPC, mHSPC, or nmCRPC setting as their last treatment (and did not progress on more than one ARPI), based on at least 1 of the following criteria: * Serum/plasma PSA progression is defined as 2 increases in PSA measured at least 1 week apart. The minimal start value is 2.0 ng/mL; 1.0 ng/mL is the minimal starting value if confirmed rise in PSA is the only indication of progression as per PCWG3 guidelines. * Soft-tissue progression defined \[PCWG3-modified RECIST v1.1 (Eisenhauer et al 2009, Scher et al 2016)\]. * Progression of bone disease: 2 new lesions; only positivity on the bone scan defines metastatic disease to bone (PCWG3 criteria \[Scher et al 2016\]). * Participants must have ≥ 1 metastatic lesion by conventional imaging that is present at Screening/Baseline CT, MRI, or bone scan imaging obtained ≤ 28 days (about 4 weeks) prior to randomization. * Participants must have adequate organ function: Bone marrow reserve * Absolute Neutrophil Count (ANC) ≥ 1.5 × 109/L * Platelets ≥ 100 × 109/L * Hemoglobin ≥ 9 g/dL Hepatic * Total bilirubin \< 2 × the institutional upper limit of normal (ULN). For participants with known Gilbert's Syndrome ≤ 3 × ULN is permitted. * Alanine aminotransferase (ALT) or aspartate aminotransferase (AST) ≤ 3.0 × ULN OR ≤ 5.0 × ULN for participants with liver metastases * Albumin ≥ 2.5 g/dL Renal * eGFR ≥ 50 mL/min/1.73m2 using Chronic Kidney Disease Epidemiology Collaboration (CKD-EPI) equation. Exclusion Criteria: * Previous treatment with any of the following within 6 weeks of randomization: Strontium-89, Samarium-153, Rhenium-186, Rhenium-188, Radium-223, hemi-body irradiation, and Lu-DOTA radioligand therapy. * Previous PSMA-imaging RLT * Previous treatment with taxane-based chemotherapy at mCRPC settings. Taxane exposure is allowed in the mHSPC setting if more than 12 months have elapsed since the completion of this therapy. * Participants with a history of CNS metastases who are neurologically unstable, symptomatic, or receiving corticosteroids for the purpose of maintaining neurologic integrity. * Symptomatic cord compression, or clinical or radiologic findings indicative of impending cord compression. * Participant with known or suspected deleterious germline or somatic homologous recombination repair gene-mutated mCRPC, who is considered appropriate for treatment with PARP inhibitor according to the judgment of the investigator. * History of myocardial infarction, angina pectoris, or coronary artery bypass graft (CABG) within 6 months prior to ICF signature and/or clinically active significant cardiac disease * Concurrent serious acute or chronic nephropathy as determined by the principal investigator. Other protocol-defined inclusion/exclusion criteria may apply.