Inclusion Criteria

          -  Ability to understand and sign an approved informed consent form.

          -  Male adult patients (≥ 18 years of age).

          -  ECOG PS of 0 or 1.

          -  Life expectancy ≥ 6 months.

          -  Histological, pathological and/or cytological confirmation of adenocarcinoma of the
             prostate without small cell or neuroendocrine features.

          -  Previous treatment with at least one novel androgen axis drug (NAAD) (e.g.
             enzalutamide and/or abiraterone).

          -  Patients must have prior orchiectomy and/or ongoing androgen deprivation therapy and a
             castrate level of serum testosterone (<50 ng/dL or <1.7 nmol/L).

          -  Previous treatment with at least 1, but no more than 2 previous - taxane regimens. A
             taxane regimen is defined as a minimum exposure of 2 cycles of a taxane. If a patient
             has received only 1 taxane regimen, he is eligible, if refuses to receive a second
             taxane regimen, or is considered unsuitable to receive a second taxane regimen (e.g.
             intolerance).

          -  Documented progression of mCRPC, as defined according to the Prostate Cancer Working
             Group 3 (PCWG3) guidelines.

          -  Adequate bone marrow, liver, and renal function, as assessed by the following
             laboratory requirements, to be conducted within 14 days before start of study drug
             administration:

               -  Hemoglobin > 9.0 g/dL

               -  Absolute neutrophil count (ANC) > 1500/mm3

               -  White blood cell (WBC) count > 3000/mL

               -  Platelet count > 100,000 /mm*3

               -  Total bilirubin < 1,5 x upper limit of normal (ULN) (except if confirmed history
                  of Gilbert's disease)

               -  ALT and AST ≤ 2.5 x ULN

               -  Serum creatinine ≤ 1.5 X ULN and glomerular filtration rate (GFR ≥ 45 mL/min/1.73
                  m2, according to the MDRD (Modified Diet in Renal Disease) abbreviated formula.

          -  Patients with partners of childbearing potential must be willing to use highly
             effective methods of birth control for the time period between the first
             administration of BAY 2315497 Injection to at least 6 months after the last
             administration of the study drug.

          -  In the darolutamide BAY2315497 Injection combination escalation arm, patients at sites
             performing the PSMA and FDG PET/CTs should be able to tolerate the 3 radiotracer
             injections and the 3 whole body PET/CT scans.

        Exclusion Criteria

          -  Diffuse bone or bone-marrow involvement (i.e. "superscan").

          -  Spinal cord compression or known brain metastases.

          -  Known incompatibility to CT/MRI, bone scan or uncontrolled pain, which results in
             patient's lack of compliance with the CT/MRI and bone scan required for PCWG3 tumor
             assessment.

          -  Clinically significant heart disease, as evidenced by myocardial infarction, arterial
             thrombotic events in the past 6 months, severe or unstable angina, or uncontrolled
             cardiovascular history.

          -  Patients known to be affected by genetic defects linked to radiation Hypersensitivity.

          -  Known history of myelodysplastic syndrome (MDS) / leukemia or with features suggestive
             of MDS/AML at any time point.

          -  Concurrent or active cancer within the last 2 years with a distinct primary site or
             histology from the cancer being evaluated in this study, with the exception of cancer
             types with less than 30% likelihood of recurrence.

          -  Known allergies, hypersensitivity, or intolerance to the study drug including
             excipients, or to contrast agents used in the diagnostic or exploratory imaging
             procedures required per protocol.

          -  Any infection of National Cancer Institute Common Terminology Criteria for Adverse
             Events (NCI-CTCAE) Version 5.0 Grade ≥ 2.

          -  Known human immunodeficiency virus (HIV) infection.

          -  Patients who have an active hepatitis B virus (HBV) or hepatitis C virus (HCV)
             infection requiring treatment.

          -  Serious, non-healing wound, ulcer, or bone fracture.

          -  Any systemic anti-neoplastic therapy (e.g. chemotherapy, immunotherapy or biological
             therapy [including monoclonal antibodies], PARP inhibitors) within at least 30 days
             prior to day of randomization (except for Luteinizing Hormone-releasing Hormone [LHRH]
             or Gonadotropin-releasing Hormone [GnRH]).

          -  Previous high-dose chemotherapy, needing hemopoietic stem cell rescue, is prohibited.

          -  Prior major surgery (excluding prostatic biopsies) must be at least 12 weeks prior to
             study entry.

          -  Previous treatment with therapeutic PSMA-targeted agents.

          -  Previous treatment with radium-223 dichloride or other radiopharmaceuticals, including
             but not limited to strontium-89 or samarium-153.

          -  Prior definitive radiotherapy completed less than 6 weeks before start of the study
             drug administration

          -  Inability to swallow oral medications

          -  A gastrointestinal disorder or procedure which is expected to interfere significantly
             with absorption of darolutamide