A Study to Learn How Safe the Study Treatment Actinium-225-macropa-pelgifatamab (BAY3546828) is, How it Affects the Body, How it Moves Into, Through and Out of the Body, and About Its Anticancer Activity in Men With Advanced Metastatic Castration-resistant Prostate Cancer (mCRPC)

Inclusion Criteria: mCRPC with pathological confirmation of adenocarcinoma without small-cell or neuroendocrine features. Previous treatment with at least 1 Novel androgen axis drug (NAAD) (e.g., enzalutamide, apalutamide, darolutamide and/or abiraterone). Prior orchiectomy and/or ongoing androgen deprivation therapy and a castrate level of serum testosterone (<50 ng/dL or <1.7 nmol/L). Prior taxane treatment: Dose Escalation: Participants must either have had prior treatment with at least 1 but no more than 2 taxane regimens, or been deemed ineligible for or refused taxane therapy on consultation with their physician Dose Expansion Group A: Participants must have had prior treatment with at least 1 but no more than 2 taxane regimens, in the castration-resistant setting Dose Expansion Group B: Participants must not have received taxane therapy since becoming castration-resistant Dose Expansion Group C: Participants must either have had prior treatment with at least 1 but no more than 2 taxane regimens, or been deemed ineligible for or refused taxane therapy on consultation with their physician Prior treatment with 177Lu-PSMA is required for participants in Dose Expansion Group C only. Eastern Cooperative Oncology Group performance status (ECOG PS) of 0 or 1. Adequate bone marrow, hepatic, and renal function, as assessed by the following laboratory requirements within 28 days before start of study treatment: Hemoglobin ≥9.0 g/dL Absolute neutrophil count (ANC) ≥1500/mm^3 Platelet count ≥100,000/mm^3 Total bilirubin ≤1.5 x the Upper limit of normal (ULN), except if confirmed history of Gilbert's disease Alanine transaminase (ALT) and Aspartate transaminase (AST) ˂2.5 x ULN (≤5 x ULN for participants with liver involvement) Participants on a stable dose of anticoagulation therapy are allowed to participate if they have no sign of bleeding or clotting, and Prothrombin time international normalized ratio (PT/INR) and activated partial thromboplastin time (aPTT) test results are acceptable at the Investigator's discretion Estimated glomerular filtration rate (eGFR) >60 mL/min/1.73 m^2, according to the Modified Diet in Renal Disease (MDRD) abbreviated formula and creatinine clearance (CrCl) >60 mL/min based on Cockcroft-Gault formula Participants must have at least one Prostate-specific membrane antigen (PSMA)-positive distant metastatic lesion on the screening PSMA PET/CT scan using the study-designated PSMA PET tracers, as determined by the site Investigator. For eligibility purposes, a PSMA-positive lesion must have activity greater than the liver by visual assessment of the screening PSMA PET/CT. A PSMA-positive metastatic lesion should not correspond to a normal tissue structure or benign lesion. Exclusion Criteria: Participants who have any of the following tumor lesions which are PSMA negative AND meet the size criteria below are excluded as determined by the site investigator. A PSMA-negative lesion for eligibility purposes must have activity equal to or less than the liver by visual assessment of the screening PSMA PET/CT scan using the study-designated PSMA PET/CT tracers. A PSMA-negative metastatic lesion should not correspond to a normal tissue structure or benign lesion. a. Any single or multiple lymph node(s) ≥2.5cm in the short axis. b. Any solid organ metastasis (e.g., lung, liver, adrenal glands, etc.) that is ≥1 cm in the short axis. c. Any bone metastasis with a soft tissue component ≥ 1cm in short axis with the soft tissue component being PSMA-negative. PSMA-negative osseous metastases without a soft tissue component do not exclude a participant. d. Predominantly necrotic lesions with greater than 1cm of enhancing tissue on contrast-enhanced Computer tomography / magnetic resonance imaging (CT/MRI). Prior systemic anticancer therapy including chemotherapy, NAAD, biologic therapy, immunotherapy, or investigational therapies within 4 weeks of the start of study treatment, except luteinizing hormone-releasing hormone (LHRH) or gonadotropin-releasing hormone (GnRH). Start of study treatment is allowed in shorter timeframes if 5 half-lives of the prior drug(s) have elapsed. Prior radiopharmaceutical treatment using 225Ac. Other prior radiopharmaceutical treatments: Dose escalation and Dose expansion Groups A and B: Prior treatment with a radiopharmaceutical is prohibited. Dose expansion Group C: Prior treatment with a radiopharmaceutical is prohibited with the following exceptions: Prior treatment with radium-223 dichloride more than 3 months before the start of study treatment is permitted; and prior treatment with 177Lu PSMA more than 6 weeks before the start of study treatment is required. Prior definitive therapy (radiotherapy or surgery) completed less than 6 weeks before the start of study treatment. Note that palliative radiotherapy completed less than 6 weeks before the start of study treatment will be allowed if: (i) no more than 10% of the participants' bone marrow is irradiated, (ii) it does not encompass all potential target/measurable lesions for participants in dose expansion. Toxic effects of Common Terminology Criteria for Adverse Events (CTCAE) Grade ≥2 from prior anticancer therapy not yet stabilized or where significant post-treatment toxicities have been observed. Chronic toxic effects of CTCAE Grade ≤2 from prior anticancer therapy where no further resolution is expected do not require exclusion with agreement between the Investigator and Sponsor (e.g., chemotherapy-induced neuropathy, fatigue, alopecia, anorexia, etc.).