This is a Phase II/III study. Patient population is adult participants with PSMA-positive mCRPC who had treatments with androgen receptor pathway inhibitor (ARPI) and taxane-based chemotherapy and progressed on or after [177Lu]Lu-PSMA targeted therapy.

Treatment of interest: the investigational treatment is AAA817 regardless of subsequent anti-neoplastic treatment. The control treatment is investigator's choice of Standard of Care, regardless of subsequent anti-neoplastic treatment

Study CAAA817A12201 consists of 2 parts: a randomized, open-label, international, multicenter, phase II study (Phase II) to collect more information to support the proposed dose of AAA817 and a randomized, open-label, international, multicenter, 2- arm phase III study (Phase III) aimed to evaluate the efficacy and safety of proposed dose of AAA817 vs. investigator's choice of standard of care (SoC) in the treatment of adult participants with PSMA-positive metastatic castration-resistant prostate cancer (mCRPC) who had treatments with ARPI and taxane-based chemotherapy, and progressed on or after [177Lu]Lu-PSMA targeted therapy. The purpose of the phase II part (Phase II) of this study is to collect additional information to support proposed phase III dose of AAA817.

Inclusion Criteria: ∙

• adults ≥ 18 years of age.
• ECOG performance status of 0 to 2.
• histopathological and/or cytological confirmation of adenocarcinoma of the prostate.
• PSMA-positive disease as assessed by PSMA PET/CT scan using an approved PSMA imaging agent as protocol instructed,
• castrate level of serum/plasma testosterone (< 50 ng/dL or < 1.7 nmol/L).
• Prior treatments with an androgen receptor pathway inhibitor (ARPI) and taxane-based chemotherapy, and progressed on or after [177Lu]Lu-PSMA targeted therapy.
• ≥ 1 metastatic lesion that is present on screening/baseline CT, MRI, or bone scan imaging obtained ≤ 28 days prior to randomization
• eGFR as requested by the sponsor

Exclusion Criteria:

• Any investigational agents within 28 days prior to the day of randomization.
• Any 225Ac-based investigational compound used prior to the day of randomization.
• Participants with a history of CNS metastases who are neurologically unstable, symptomatic, or receiving corticosteroids for the purpose of maintaining neurologic integrity.
• Concurrent acute kidney injury (renal failure developed between 48 hours to 7 days) or chronic kidney disease (at least 3 months of ongoing renal injury)
• Baseline xerostomia ≥ Grade 2 by CTCAE v.5
• History of uncontrolled hypertension, myocardial infarction (MI), angina pectoris, or coronary artery bypass graft (CABG) within 6 months prior to ICF signature and/or clinically active significant cardiac disease
• History of lymphoproliferative disease or any known malignancy or history of malignancy of any organ system within the past 5 years (except for basal cell carcinoma or actinic keratosis that have been treated with no evidence of recurrence in the past 3 months, non-invasive malignant colon polyps that have been removed).

Other protocol-defined inclusion/exclusion criteria may apply.