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 Participants With Advanced Metastatic Castration-resistant Prostate Cancer (mCRPC)

Inclusion Criteria:

• mCRPC with pathological confirmation of adenocarcinoma without small-cell orneuroendocrine 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 levelof serum testosterone (<50 ng/dL or <1.7 nmol/L).

• Prior taxane treatment:

• Dose Escalation: Participants must either have had prior treatment with atleast 1 but no more than 2 taxane regimens, or been deemed ineligible for orrefused taxane therapy on consultation with their physician

• Dose Expansion Group A: Participants must have had prior treatment with atleast 1 but no more than 2 taxane regimens, in the castration-resistant setting

• Dose Expansion Group B: Participants must not have received taxane therapysince becoming castration-resistant

• Dose Expansion Group C: Participants must either have had prior treatment withat least 1 but no more than 2 taxane regimens*, or been deemed ineligible foror refused taxane therapy on consultation with their physician *A taxaneregimen consists of a minimum of 2 treatment cycles (maximum number of cyclesas per local guidelines). A treatment break within a taxane regimen may begiven provided that another anticancer therapy is not administered during thattime

• Prior treatment with an established 177Lu-PSMA therapy (i.e., dose activity andcycles comparable to approved treatments) is required for participants in DoseExpansion Group C only. More specifically, to qualify for this expansion group,participants must not have discontinued 177Lu-PSMA tratment due to intolerance.

• Eastern Cooperative Oncology Group performance status (ECOG PS) of 0 or 1.

• Adequate bone marrow, hepatic, and renal function, as assessed by the followinglaboratory requirements within 30 days before start of study intervention:

• 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), or <= 3 ULN if theparticipant has a confirmed history of Gilbert's syndrome (note thatparticipants with Gilbert's syndrome should be carefully evaluated for otherliver-related disorders that may impact their suitability for this study).

• Alanine transaminase (ALT) and Aspartate transaminase (AST) ˂2.5 x ULN (≤5 xULN for participants with liver involvement)

• Participants on a stable dose of anticoagulation therapy are allowed toparticipate if they have no sign of bleeding or clotting, and Prothrombin timeinternational normalized ratio (PT/INR) and activated partial thromboplastintime (aPTT) test results are acceptable at the Investigator's discretion

• Estimated glomerular filtration rate (eGFR) >60 mL/min/1.73 m^2, according tothe Modified Diet in Renal Disease (MDRD) abbreviated formula and creatinineclearance (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 usingthe study-designated PSMA PET tracers, as determined by the site Investigator. Foreligibility purposes, a PSMA-positive lesion must have activity greater than theliver by visual assessment of the screening PSMA PET/CT. A PSMA-positive metastaticlesion should not correspond to a normal tissue structure or benign lesion.

• Documented progressive mCRPC per PCWG3, defined as meeting at least one of thefollowing criteria:

• PSA-progression (defined as 2 consecutive increases over a previous referencevalue obtained at a minimum of 1-week intervals, with a minimum starting valueof 2.0 ng/mL)

• Radiological progression in soft-tissue lesions according to PCWG3 modificationof RECIST v1.1 criteria

• Progression of bone disease (defined as ≥2 new bone lesions according to PCWG3bone scan criteria).

• Documented progressive mCRPC per PCWG3 and a minimun starting PSA value of 2.0ng/mL is mandatory. Progressive mCRPC is defined as meeting at least one of thefollowing criteria: a. PSA progression (defined as 2 consecutive increases overa previous reference value obtained at a minimun of 1-week intervals). b.Radiological progression in soft-tissue lesions according to PCWG3 modificationof RECIST v1.1 criteria. c. Progression of bone disease (defined as ≥ 2 newbone lesions according to PCWG3 bone scan criteria).

Exclusion Criteria:

• Participants who have any of the following tumor lesions which are PSMA negative ANDmeet the size criteria below are excluded as determined by the site investigator. APSMA-negative lesion for eligibility purposes must have activity equal to or lessthan the liver by visual assessment of the screening PSMA PET/CT scan using thestudy-designated PSMA PET/CT tracers. A PSMA-negative metastatic lesion should notcorrespond 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 withthe soft tissue component being PSMA-negative. PSMA-negative osseous metastaseswithout a soft tissue component do not exclude a participant.

• d. Predominantly necrotic lesions with greater than 1cm of enhancing tissue oncontrast-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 studyintervention, except luteinizing hormone-releasing hormone (LHRH) orgonadotropin-releasing hormone (GnRH). Start of study intervention is allowed inshorter timeframes if 5 half-lives of the prior drug(s) have elapsed.

• Prior radiopharmaceutical treatment using actinium-225.

• Other prior radiopharmaceutical treatments:

• Dose escalation and Dose expansion Groups A and B: Prior treatment with aradiopharmaceutical is prohibited.

• Dose expansion Group C: Prior treatment with a radiopharmaceutical isprohibited with the following exceptions: Prior treatment with radium-223dichloride more than 3 months before the start of study intervention ispermitted; and prior treatment with 177Lu PSMA more than 6 weeks before thestart of study intervention is required.

Note: Participants who have discontinued 177Lu-PSMA treatment due to intolerance are excluded from Group C.

• Prior definitive therapy (radiotherapy or surgery) completed less than 6 weeksbefore the start of study intervention. Note that palliative radiotherapy completedless than 6 weeks before the start of study intervention will be allowed if: (i) nomore than 10% of the participants' bone marrow is irradiated, (ii) it does notencompass all potential target/measurable lesions for participants in doseexpansion.

• Toxic effects of Common Terminology Criteria for Adverse Events (CTCAE) Grade ≥2from prior anticancer therapy not yet stabilized or where significant post-treatmenttoxicities have been observed. Chronic toxic effects of CTCAE Grade ≤2 from prioranticancer therapy where no further resolution is expected do not require exclusionwith agreement between the Investigator and Sponsor (e.g., chemotherapy-inducedneuropathy, fatigue, alopecia, anorexia, etc.).

• Dose Expansion (Groups A, B and C): Presence of >3 liver metastases, any diffuseliver metastasis, or PSMA-non-avid liver metastasis (uptake is lower or equalcompared to healthy liver tissue).