A Study of AZD4635 With Durvalumab and With Cabazitaxel and Durvalumab in Patients With mCRPC.

Inclusion Criteria:

1. Histologically confirmed adenocarcinoma of the prostate.
2. Known castrate-resistant disease.
3. Evidence of disease progression ≤6 months.
4. Body weight \>30 kg at screening.
5. Willingness to adhere to the study treatment-specific contraception requirements.
6. Adequate bone marrow reserve and organ function.
7. Adequate organ function for Arm A as demonstrated by all of the following laboratory values:

   * Alanine aminotransferase (ALT) ≤2.5 × upper limit of normal (ULN) if no demonstrable liver metastases or ≤5 × ULN in the presence of liver metastases.
   * Aspartate aminotransferase (AST) ≤2.5 × ULN if no demonstrable liver metastases or ≤5 × ULN in the presence of liver metastases
   * Total bilirubin (TBL) ≤1.5 × ULN
   * TBL ≤2.0 × ULN in the case of known Gilbert syndrome with normal direct bilirubin
8. Participants in Arm A must have received the following prior therapy:

   * Maximum of 3 lines of therapy in the mCRPC setting
   * Prior therapy with one or more NHAs (eg, abiraterone acetate, enzalutamide, apalutamide, darolutamide) in either hormone-sensitive or hormone-refractory settings
   * Prior therapy with one or more lines of taxanes (eg, docetaxel and/or cabazitaxel)
   * Alternatively, must be taxane-ineligible
   * Prior therapy can be in either the hormone-sensitive or the hormone-refractory setting
9. Adequate organ function for Arm B as demonstrated by all of the following laboratory values:

   * AST and/or ALT ≤1.5 × ULN
   * TBL ≤ ULN
   * TBL ≤2.0 × ULN in the case of known Gilbert syndrome with normal direct bilirubin
10. Participants in Arm B must have received the following prior therapy:

    * Prior docetaxel (taxane) in either hormone-sensitive or hormone-refractory settings
    * Received no prior cytotoxic chemotherapy other than docetaxel for prostate cancer except for estramustine and except adjuvant/neo-adjuvant treatment completed \>3 years ago.
    * Prior therapy with only one NHAs (eg, abiraterone acetate or enzalutamide; prior apalutamide is not permitted) for treatment of mCRPC in either hormone-sensitive or hormone-refractory settings.
    * Be suitable to receive concomitant Granulocyte-colony stimulating factor during all cycles of cabazitaxel.
    * Participants who meet inclusion criteria for Arm B will be allocated preferentially to that arm until recruitment to that arm is completed.

Exclusion Criteria:

1. Active brain metastases or leptomeningeal metastases.
2. There must be no requirement for immunosuppressive doses of systemic corticosteroids for at least 2 weeks prior to study enrollment.
3. History of pneumonitis requiring corticosteroids, second malignancy that is progressing and/or received active treatment ≤3 years before the first dose of study intervention, and hypersensitivity to polysorbate-80 if allocated to cabazitaxel.
4. As judged by the Investigator, any evidence of severe or uncontrolled systemic diseases.
5. Creatinine clearance \<40 mL/min (calculated by Cockcroft-Gault equation).
6. Prior exposure to immune-mediated therapy including.
7. Ongoing treatment with warfarin (Coumadin).
8. Major surgery (excluding placement of vascular access) within 4 weeks of the first dose of study intervention.