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 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 \*A taxane regimen consists of a minimum of 2 treatment cycles (maximum number of cycles as per local guidelines). A treatment break within a taxane regimen may be given provided that another anticancer therapy is not administered during that time
* Prior treatment with an established 177Lu-PSMA therapy (i.e., dose activity and cycles comparable to approved treatments) is required for participants in Dose Expansion 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 following laboratory 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 the participant has a confirmed history of Gilbert's syndrome (note that participants with Gilbert's syndrome should be carefully evaluated for other liver-related disorders that may impact their suitability for this study).
  * 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.
* Documented progressive mCRPC per PCWG3, defined as meeting at least one of the following criteria:

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

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 intervention, except luteinizing hormone-releasing hormone (LHRH) or gonadotropin-releasing hormone (GnRH). Start of study intervention is allowed in shorter 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 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 intervention is permitted; and prior treatment with 177Lu PSMA more than 6 weeks before the start 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 weeks before the start of study intervention. Note that palliative radiotherapy completed less than 6 weeks before the start of study intervention 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.).
* Dose Expansion (Groups A, B and C): Presence of \>3 liver metastases, any diffuse liver metastasis, or PSMA-non-avid liver metastasis (uptake is lower or equal compared to healthy liver tissue).