Cabazitaxel in Combination With 177Lu-PSMA-617 in Metastatic Castration-resistant Prostate Cancer

Inclusion Criteria: 1. Male patients aged 18 years or older at the time of informed consent. 2. Patient has provided written informed consent. 3. Histologically confirmed adenocarcinoma of the prostate without neuroendocrine or small cell differentiation. 4. Eastern Cooperative Oncology Group (ECOG) performance status of ≤ 1 5. Patients must have had prior treatment with docetaxel. 6. Patients must have progressed on a second-generation androgen receptor (AR)-targeted agent (e.g., enzalutamide, abiraterone, or apalutamide) in the castrate-resistant setting. 7. Patients must have progressive disease. The Prostate Cancer Clinical Trials Working Group 3 (PCWG3) defines this as any one of the following: 1. PSA progression: minimum of two rising PSA values from a baseline measurement with an interval of ≥ 1 week between each measurement 2. Soft tissue or visceral disease progression as per Response Evaluation Criteria in Solid Tumours version 1.1 (RECIST 1.1) criteria 3. Bone progression: ≥ 2 new lesions on bone scan 8. At least three weeks since the completion of surgery prior to registration. 9. Prior surgical orchiectomy or chemical castration maintained on luteinizing hormone-releasing hormone (LHRH) analogue (agonist or antagonist). 10. Serum testosterone levels ≤ 1.75nmol/L within 28 days prior to registration. 11. Imaging evidence of metastatic disease documented with either whole body bone scan (WBBS) or computed tomography (CT) scan performed within 28 days prior to registration. 12. Significant prostate-specific membrane antigen (PSMA) avidity on PSMA PET/CT, defined as a minimum uptake of SUVmax 15 at a site of disease. 13. Patients must have a life expectancy ≥ 12 weeks. 14. Assessed by a medical oncologist as suitable for treatment with cabazitaxel and 177Lu-PSMA-617. 15. Patients must have adequate bone marrow, hepatic and renal function documented within 28 days prior to registration, defined as: 1. Haemoglobin ≥ 90 g/L independent of transfusions (no red blood cell transfusion in last 28 days prior to registration) 2. Absolute neutrophil count (ANC) ≥ 1.5x10\^9/L 3. Platelets ≥ 150 x10\^9/L 4. Total bilirubin ≤ 1.5 x upper limit of normal (ULN) except for patients with known Gilbert's syndrome, where this applies for the unconjugated bilirubin component 5. Aspartate transaminase (AST) and alanine transaminase (ALT) ≤ 2.5 x ULN if there is no evidence of liver metastasis or ≤ 5 x ULN in the presence of liver metastases 6. Albumin ≥ 25 g/L 7. Adequate renal function: patients must have a creatinine clearance estimated of ≥ 40 mL/min using the Cockcroft-Gault equation 16. Sexually active patients are willing to use medically acceptable forms of barrier contraception. 17. Willing and able to comply with all study requirements, including all treatments and the timing and nature of all required assessments. Exclusion Criteria: 1. Superscan on WBBS or diffuse marrow disease on PSMA PET. 2. Site(s) of measurable disease that are FDG-positive with low PSMA expression (SUVmax \<10). 3. Prior treatment with cabazitaxel or 177Lu-PSMA-617. 4. Contraindications to the use of corticosteroid treatment. 5. Other malignancies within the previous 2-years other than basal cell or squamous cell carcinomas of skin or other cancers that are unlikely to recur within 24 months. 6. Presence of untreated brain metastases or leptomeningeal metastases. 7. Patients with symptomatic or impending cord compression unless appropriately treated beforehand and clinically stable for ≥ four weeks. 8. Concurrent illness, including severe infection that may jeopardise the ability of the patient to undergo the procedures outlined in this protocol with reasonable safety. 9. Persistent toxicities (CTCAE v5.0 \>/= Grade 2) caused by previous cancer therapy, excluding alopecia. 10. Known HIV or hepatitis B or C infection. 11. Radiotherapy or systemic anti-cancer therapies administered within 14 days prior to registration, excluding androgen deprivation therapy (ADT).