A Study of Pasritamig With or Without JNJ-87189401 Versus Placebo for Late Line Metastatic Castration-resistant Prostate Cancer (mCRPC)

Inclusion Criteria

* Histologically confirmed adenocarcinoma of the prostate
* Metastatic castration-resistant prostate cancer (mCRPC): Disease that is metastatic either to bone, any lymph node, or both without clear evidence of other metastatic sites at the time of screening by conventional imaging with computed tomography (CT) or magnetic resonance imaging (MRI) (chest, abdomen, and pelvis) and 99m\^Tc bone scan. Visceral disease is not allowed
* PSA greater than or equal to (≥) 2 nanogram per milliliter (ng/mL) at screening
* In the opinion of the investigator, the next best treatment option is a clinical trial
* Participants are required to have had all life-prolonging therapies for which they are clinically eligible in the opinion of the investigator and to which they have access. Prior therapies could have been given in any disease setting (not limited to mCRPC). In particular, prior treatment specifications include receipt of the following:

Androgen-receptor pathway inhibitor (ARPI): Must have progressed on at least 1 ARPI and unlikely to benefit from retreatment with another ARPI

Taxanes: Required to have received at least 2 previous taxane-based regimens. If a participant has received only 1 taxane regimen, the participant is eligible if:

1. Cabazitaxel is not available
2. The participant's physician deems the participant unsuitable to receive a second taxane regimen due to toxicity risk or prior intolerance Note: a taxane-based regimen consists of at least 2 cycles of a taxane (either as a single agent or in combination with other therapies) administered within the same 2-month period

Radioligand therapy: Required to have been previously treated with at least 1 dose of Prostate-specific membrane antigen (PSMA)-targeted lutetium radioligand therapy (eg, lutetium Lu-177 vipivotide tetraxetan), unless one of the following applies:

1. PSMA-targeted lutetium radioligand therapy is unavailable, not accessible, or not clinically indicated.
2. The participant's physician deems the participant unsuitable to receive PSMA-targeted lutetium radioligand therapy.

Polyadenosine diphosphate-ribose polymerase inhibitors (PARPi): Required to have been previously treated with PARPi, if the participant has a known germline or somatic BRCA mutation and treatment is available

* Prior orchiectomy or medical castration (receiving ongoing ADT with a GnRH analog \[agonist or antagonist\]) prior to the first dose of study treatment and must continue this therapy throughout the treatment phase
* Eastern Cooperative Oncology Group (ECOG) performance status of 0 to 2
* Participants are eligible if they have the following values:

A) eGFR ≥ 40 milliliters per minute (mL/min) B) Alanine Aminotransferase (ALT) and Aspartate Aminotransferase (AST) less than or equal to (≤) 3 times the Upper Limit of Normal (ULN) C) Total bilirubin \<1.5 times ULN D) Absolute neutrophil count (ANC) ≥ 1.0x10\^9/per liter (L) E) Hemoglobin ≥ 8.0 grams per deciliter (g/dL) F) Platelet count ≥ 75x10\^9/L

Exclusion Criteria

* Venous thromboembolic events within 1 month prior to the first dose of study treatment; uncomplicated (Grade ≤ 2) deep vein thrombosis is not exclusionary
* Active autoimmune disease within the past 12 months that requires systemic immunosuppressive medications (eg, chronic corticosteroid, methotrexate, or tacrolimus)
* Participants with Grade 1 or higher fever (≥38ºC) or active infection requiring systemic treatment within 7 days prior to randomization are ineligible. Participants must be afebrile (\<38ºC) at the time of study treatment dosing unless approved by medical monitor
* Clinically significant pulmonary compromise, particularly a requirement for supplemental oxygen use (\>2 liters per minute (L/min) by nasal cannula) to maintain adequate oxygenation
* Prior or concurrent second malignancy (other than the disease under study) for which natural history or treatment could likely interfere with any study endpoints of safety or the efficacy of the study treatment(s)
* Any of the following within 6 months prior to first dose of study treatment:

A) Myocardial infarction B) Severe or unstable angina C) Clinically significant ventricular arrhythmias D) Congestive heart failure (New York Heart Association class II to IV) E) Transient ischemic attack F) Cerebrovascular accident

\- Prior treatment with any CD3-directed therapy