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

Inclusion Criteria: 1. Participants with a diagnosis of histologically confirmed adenocarcinoma of the prostate (no small cell, neuroendocrine, sarcomatoid, spindle or signet cell). 2. Minimum life expectancy of 3 months or more. 3. Eastern Cooperative Oncology Group (ECOG) performance status of O or 1 at screening, with no deterioration. 4. PCWG3 (Prostate Cancer Working Group 3) modified RECIST Version 1.1 evaluable disease. 5. Must have received at least one novel androgen receptor pathway inhibitor (ARPI), such as enzalutamide or darolutamide or apalutamide or abiraterone acetate. 6. Must have one or more unresectable metastatic lesions. 7. Must have had prior orchiectomy and/or ongoing androgen deprivation therapy, and a castrate level of serum testosterone (\<50ng/dL or \<l.7nmol/L). 8. Progressive metastatic castration-resistant prostate cancer (mCRPC) following the most recent treatment at time of study entry. 9. Adequate organ and marrow function. 10. Non sterilised participants who are sexually active with a partner of childbearing potential must use a condom (plus spermicide, if available), must refrain from fathering a child, freezing or donating sperm, and it is recommended for the partner to also use a highly effective contraceptive method. Inclusion Criteria for Sub study 1: 1. Must have received a single line of ARPI, such as enzalutamide, darolutamide, apalutamide or abiraterone acetate. Participants who were exposed to more than one ARPI due to toxicity or intolerance (not due to disease progression) are eligible. 2. PSMA positive mCRPC by computed tomography positron emission tomography, obtained with PSMA ligand defined as at least 1 PSMA positive metastatic lesion with tracer uptake greater than liver, and no PSMA negative lesions. All measurable or intraprostatic lesions must be PSMA positive. 3. Capable of self-administering oral formulations. Exclusion Criteria: 1. Any evidence of non adenocarcinomatous forms of prostate cancer (including small cell, spindle cell, signet cell, neuroendocrine, sarcomatous). 2. Known, unresolved urinary tract obstruction. 3. Participants with a history of central nervous system metastases. 4. Symptomatic malignant spinal cord compression or findings indicative of impending cord compression. 5. Participants with a history of leptomeningeal carcinomatosis. 6. Previous or concurrent cancer distinct from the cancer under investigation in primary site or histology . 7. Concurrent serious medical conditions. 8. Previous history of interstitial lung disease or non-infectious pneumonitis. 9. Participants with a history or clinical/laboratory features suggestive of myelodysplastic syndrome or acute myeloid leukaemia. 10. Persistent toxicities caused by previous therapy. 11. Participants unable to swallow orally administered medications or with gastrointestinal disorders likely to interfere with absorption. 12. Active infection, including tuberculosis, hepatitis C virus, and hepatitis B virus infection. 13. Known hypersensitivity to study intervention or any of their excipients. Exclusion Criteria for Sub study 1: 1. History of uncontrolled seizures or requirement for \>2 antiepileptic drugs. 2. History of severe brain injury or stroke. 3. Skeletal metastases demonstrating a superscan appearance on bone scan. 4. Participants have received prior therapy with palacaparib (AZD9574) or more than 1 prior line of any other Poly-ADP-ribose polymerase inhibitor (PARPi)-based regimen (either as a treatment or as maintenance).