Pembrolizumab, Carboplatin and Cabazitaxel in Aggressive Metastatic Castration Resistant Prostate Cancer (PEAPOD_FOS)

Inclusion Criteria: * Male participants who are at least 18 years of age on the day of signing informed consent * Histologically confirmed diagnosis of adenocarcinoma and/or neuroendocrine carcinoma of the prostate will be enrolled in this study * Presence of metastatic disease documented on imaging studies (bone scan, computed tomography (CT) and/or magnetic resonance imaging (MRI) scans * At least one of the following Aggressive Variant Prostate Cancer (AVPC) Criteria 1. Histologically proven small cell (neuroendocrine) prostate cancer 2. Exclusive visceral metastases 3. Predominantly lytic bone metastases 4. Bulky lymph nodes (≥ 5 cm in longest dimension) or high-grade pelvic/prostatic masses 5. Low PSA (≤10 ng/ml) at initial presentation in the presence of extensive disease (≥20 metastases) 6. Elevated serum Lactate Dehydrogenase (LDH) (≥2 x ULN) or carcinoembryonic antigen (CEA) (≥2 x Upper limit (UL)) 7. Short time to castration-resistance (≤6 months). * Male participants: a male participant must agree to use a contraception as detailed in Appendix 3 of the protocol during the treatment period and for at least after the last dose of study treatment and refrain from donating sperm during this period * The participant (or legally acceptable representative if applicable) provides written informed consent for the trial. * Have measurable disease based on RECIST 1.1. Lesions situated in a previously irradiated area are considered measurable if progression has been demonstrated in such lesions. * Have provided archival tumor tissue sample obtained in the previous year since or newly obtained core or excisional biopsy of a tumor lesion not previously irradiated. Formalin-fixed, paraffin embedded (FFPE) tissue blocks are preferred to slides. Newly obtained biopsies are preferred to archived tissue. * Have an Eastern Cooperative Oncology Group (ECOG) performance status of 0 to 1. Evaluation of ECOG is to be performed within 7 days prior to the first dose of study intervention. * Have adequate organ function as defined in the table 1 of the protocol. Specimens must be collected within 10 days prior to the start of study intervention. * Criteria for known Hepatitis B (HBV) and C (HCV) positive subjects 1. Hepatitis B and C screening tests are not required unless: * Known history of HBV or HCV infection * As mandated by local health authority 2. Hepatitis B positive subjects * Participants who are HBsAg positive are eligible if they have received HBV antiviral therapy for at least 4 weeks and have undetectable HBV viral load prior to randomization. * Participants should remain on anti-viral therapy throughout study intervention and follow local guidelines for HBV anti-viral therapy post completion of study intervention. 3. Participants with history of HCV infection are eligible if HCV viral load is undetectable at screening. • Participants must have completed curative anti-viral therapy at least 4 weeks prior to randomization. Exclusion Criteria: * Has received prior therapy with an anti-PD-1, anti-PD-L1, or anti-PD-L2 agent or with an agent directed to another stimulatory or co-inhibitory T-cell receptor (e.g., Cytotoxic T-Lymphocyte Antigen 4 (CTLA-4), OX-40, CD137). * Has received prior systemic anti-cancer therapy including investigational agents within 4 weeks prior to informed consent signature. * Has received previous treatment with cabazitaxel or carboplatin. * Has received prior radiotherapy within 2 weeks of start of study intervention. Participants must have recovered from all radiation-related toxicities, not require corticosteroids, and not have had radiation pneumonitis. A 1-week washout is permitted for palliative radiation (≤2 weeks of radiotherapy) to non-central nervous system (non-CNS) disease. * Has received a live vaccine or live-attenuated vaccine within 30 days before the first dose of study intervention. Administration of killed vaccines is allowed. * Is currently participating in or has participated in a study of an investigational agent or has used an investigational device within 4 weeks prior to the first dose of study intervention. * Has a diagnosis of immunodeficiency or is receiving chronic systemic steroid therapy (in dosing exceeding 10 mg daily of prednisone equivalent) or any other form of immunosuppressive therapy within 7 days prior to the first dose of study drug. * Known additional malignancy that is progressing or has required active treatment within the past 5 years. Note: Participants with basal cell carcinoma of the skin, squamous cell carcinoma of the skin or carcinoma in situ, excluding carcinoma in situ of the bladder, that have undergone potentially curative therapy are not excluded. * Has known active CNS metastases and/or carcinomatous meningitis. Participants with previously treated brain metastases may participate provided they are radiologically stable, i.e. without evidence of progression for at least 4 weeks by repeat imaging (note that the repeat imaging should be performed during study screening), clinically stable and without requirement of steroid treatment for at least 14 days prior to first dose of study intervention. * Has severe hypersensitivity (≥Grade 3) to pembrolizumab, carboplatin or cabazitaxel and/or any of its excipients. * Has active autoimmune disease that has required systemic treatment in the past 2 years (i.e., with use of disease modifying agents, corticosteroids or immunosuppressive drugs). Replacement therapy (eg., thyroxine, insulin, or physiologic corticosteroid replacement therapy for adrenal or pituitary insufficiency, etc.) is not considered a form of systemic treatment and is allowed. * Has a history of (non-infectious) pneumonitis/interstitial lung disease that required steroids or has current pneumonitis/interstitial lung disease. * Has an active infection requiring systemic therapy * Has congestive Heart failure New York Heart Association (NYHA) ≥2. * Has hypoacusis grade ≥2. * Has a known history of Human Immunodeficiency Virus (HIV) infection * Concurrent active Hepatitis B (defined as HBsAg positive and/or detectable HBV DNA) and Hepatitis C virus (defined as anti-HCV Ab positive and detectable HCV RNA) infection. Note: Hepatitis B and C screening tests are not required unless: * Known history of HBV and HCV infection * As mandated by local health authority * Has a history or current evidence of any condition, therapy, or laboratory abnormality or other circumstance that might confound the results of the study, interfere with the participant's participation for the full duration of the study, such that it is not in the best interest of the participant to participate, in the opinion of the treating investigator. * Has known psychiatric or substance abuse disorders that would interfere with cooperation with the requirements of the trial. * Has had an allogenic tissue/solid organ transplant.