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)

Researchers are looking for a better way to treat people who have advanced metastatic castration-resistant prostate cancer (mCRPC). In participants with metastatic castration-resistant prostate cancer (mCRPC), the cancer of the prostate has spread to other parts of the body (metastatic) and does not respond to the lowering of testosterone levels in the body (castration resistant). The cancer is 'advanced' and is unlikely to be cured or controlled with currently available treatments. Despite new treatment options for participant(s) with prostate cancer in recent years, the cancer often returns and worsens. The study treatment actinium-225-macropa-pelgifatamab (also called 225Ac-pelgi or BAY3546828) is a new type of treatment under development for participants with mCRPC who have already received available treatments or have few treatment options available. It works by binding to a protein on the surface of the cancer cells called prostate specific membrane antigen (PSMA). As it gives off a type of radioactivity that travels a very short distance, it kills the nearby (cancer) cells that express PSMA. The main purpose of this first-in-human study in participants with mCRPC is to learn: * How safe different doses of 225Ac-pelgi are. * To what degree medical problems caused by 225Ac-pelgi can be tolerated by the participants? * Which dose of 225Ac-pelgi is optimal for treatment (safe and working well)? * How good is 225Ac-pelgi's anticancer activity? To answer this, the researchers will look at: * The number and severity of medical problems that the participants have after treatment with 225Ac-pelgi (per dose level). * The ratio of medical problems and anticancer activity per dose. * Anticancer activity of the optimal 225Ac-pelgi dose as proportion of participants who have at least halved prostate-specific antigen (PSA) levels after 12 weeks of treatment or later and/or shrunken or no longer detectable tumors. * The lowest PSA level reached after treatment start. Doctors keep track of all medical problems (also called adverse events) that participants have during the study, even if they do not think that they might be related to the study treatment. Anticancer activity is measured using cancer imaging techniques and change in blood level of a protein called PSA. PSA is made by normal and by cancerous cells in the body. The PSA level is taken as a marker for prostate cancer development and is usually elevated in participants with mCRPC. In addition, researchers want to find out how 225Ac-pelgi moves into, through and out of the body. The study will have two parts. The first part, called dose escalation, is done to find the most appropriate dose and schedule that can be given in the second part of the study. For this, each participant will receive one of the predefined increasing doses of 225Ac-pelgi as an infusion into the vein. All participants in part 2, called dose expansion, will receive the most appropriate dose and schedule identified from the first part of the study. More than one dose level or schedule from part 1 may be tested. Both the participants and the study team know what treatment the participants will take. Participants in this study will take the study treatment 225Ac-pelgi once in a period of 6 weeks called a cycle. Each participant will have 4 of these treatment cycles, if the participant benefits from the treatment. Each participant will be in the study for up to nearly six years, including a first test (screening) phase of a maximum of 30 days, up to 12 months of treatment depending on the participant's benefit, and a follow-up phase of 60 months after the end of treatment. The following visits to the study site are planned: 2 during the screening phase, 8 in the first treatment cycle, 7 in subsequent cycles, and a visit 6 to 12 weeks after the last dose. In the following 12 months, visits are planned every 6 weeks and during the next 48 months phone calls or clinic visits are planned approximately every 12 weeks. In addition, a sub study during the dose escalation part will gather information on the distribution of the study treatment in the body, the proportion that binds to the cancer cells, and the resulting radiation at the tumor site. During the study, the study team will: * Do physical examinations * Check vital signs such as blood pressure, heart rate, and body temperature * Take blood, and urine samples * Examine heart health using echocardiogram and electrocardiogram (ECG) * Take tumor samples * Track 225Ac-pelgi in the body using gamma imaging (generally available at all study sites) * Check the tumor status using PET (positron emission tomography), CT (computed tomography) or MRI (magnetic resonance imaging) and bone scan * Ask questions about the impact of the disease on the participants' wellbeing and activities of daily life (Eastern Cooperative Oncology Group Performance status (ECOG PS)).

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).