Phase Ib/II Platform Study of Multiple Anti-Cancer Agents in Participants With Metastatic Prostate Cancer

This is a multicentre, open-label and platform study to evaluate multiple anti-cancer agents in participants with metastatic prostate cancer. This platform study will comprise a series of substudies. Each substudy will follow a 2-part structure (unless otherwise stated in the individual substudy): * Part A: A dose escalation (DE) phase to identify dose limiting toxicities (DLTs), characterise safety, PK, pharmacodynamics, preliminary efficacy, and determine biologically and clinically suitable dose levels to proceed into the dose optimisation/expansion. * Part B: A dose optimisation/expansion phase to inform recommended Phase 3 dose (RP3D), explore efficacy with Prostate-specific antigen (PSA) decrease ≥ 50% (PSA50) rate as primary endpoints, alongside continued safety monitoring. Sub-study 1 focuses on a specific combination regimen and it will assess the safety, tolerability, PK, pharmacodynamics, and preliminary anti-tumour activity of AZD2265 (FPI-2265) actinium (225Ac) zadavotide guraxetan \[hereafter referred to as AZD2265 (FPI-2265)\] in combination with palacaparib (AZD9574) compared with AZD2265 (FPI-2265) monotherapy and with standard-of-care (SoC) docetaxel chemotherapy in participants with metastatic castration resistant prostate cancer (mCRPC).