Bipolar Androgen Therapy + Carboplatin in mCRPC

Inclusion Criteria: 1. Males with histologically confirmed adenocarcinoma of the prostate 2. Confirmed HRD (Homologous recombination defect) in germline and/or somatic DNA analysis (tumour or blood), by a validated assay (see Appendix 1). Mutations in HR genes not listed in appendix 1 will be considered in literature suggests pathogenicity. A maximum of 10 uncharacterised or heterozygous mutations will be included. 3. Age ≥ 18 years 4. ECOG performance status ≤ 1 5. Rising PSA confirmed on two sequential tests ≥1 week apart and a minimum value of 2 ug/L despite castrate levels of testosterone 6. Serum testosterone \< 1.7 nmol/L and on an LHRH agent or post orchidectomy ≥ 1 year. 7. Washout of ≥ 4 weeks from prior line of treatment, radiotherapy or surgery (aside from LHRH agent) 8. Adequate bone marrow function (platelets \> 100 x 109/L, ANC \> 1.5 x 109/L, Hb \>100) 9. Adequate liver function (ALT/AST \< 1.5 x ULN, bilirubin \< 2 x ULN) 10. Adequate renal function (creatinine clearance \> 50 ml/min) 11. Adequate cardiac function and reserve after cardiology assessment 12. Archived tissue sample available or willingness to undergo fresh biopsy 13. Willing and able to comply with all study requirements, including treatment, timing and/or nature of required assessments 14. Signed, written informed consent Exclusion Criteria: 1. Contraindications to investigational product 2. Pain due to metastatic prostate cancer requiring opioid analgesics 3. Evidence of disease progression in sites or extent that, in the opinion of the investigator, would put the patient at risk from testosterone therapy and its potential for initial tumour flare (eg: femoral metastasis at risk of fracture, ureteric obstruction due to nodal disease or cord compression due to spinal metastases). 4. Previous treatment with platinum chemotherapy and/or a PARP inhibitor. However up to 8 men with prior treatment to these agents will be included as an exploratory cohort. 5. Life expectancy of less than 3 months. 6. Brain metastases or leptomeningeal disease 7. History of thromboembolic event and not currently on anticoagulation 8. Prior myocardial infarction or unstable angina within 2 years of study entry 9. Haematocrit ≥ 50%, untreated severe obstructive sleep apnoea or poorly controlled heart failure (NYHA \>1) 10. History of another malignancy within 5 years prior to registration. Patients with a past history of adequately treated carcinoma-in-situ, basal cell carcinoma of the skin, squamous cell carcinoma of the skin, or superficial transitional cell carcinoma of the bladder are eligible. Patients with a history of other malignancies are eligible if they have been continuously disease free for at least 5 years after definitive primary treatment. 11. Concurrent illness, including severe infection that may jeopardize the ability of the patient to undergo the procedures outlined in this protocol with reasonable safety. 12. Presence of any psychological, familial, sociological or geographical condition potentially hampering compliance with the study protocol and follow-up schedule, including alcohol dependence or drug abuse.