The purpose of this study is to identify the recommended phase 2 combination dose (RP2CD) of JNJ-78278343 in combination with JNJ-95298177 in Part 1 (Dose confirmation) of the study and to determine how safe and tolerable the RP2CD of JNJ-7827834 and JNJ-95298177 with or without JNJ-87189401 is for treatment of participants with metastatic castration-resistant prostate cancer (mCRPC; a stage of prostate cancer where the cancer has spread beyond the prostate and is resistant to hormonal therapy) in Part 2 (Dose expansion) of study.
Histologically confirmed adenocarcinoma of the prostate. Primary small cell carcinoma, carcinoid tumor, neuroendocrine (NE) carcinoma, or large cell NE carcinoma arising in the prostate are not allowed; however, adenocarcinomas with NE features (for example [e.g.], immunohistochemistry [IHC] with both androgen receptor [AR]- and NE-marker positivity) are allowed
Must have metastatic castration-resistant prostate cancer (mCRPC)
PSA must measure at least 2 nanograms per milliliters (ng/mL) at screening
Measurable or evaluable disease
Toxicity related to prior anticancer therapy that has not returned to grade less than or equal to (<=) 1 or baseline levels (except for alopecia and vitiligo)
Known allergies, hypersensitivity, or intolerance to any of the components (e.g., excipients) of JNJ-78278343, JNJ-95298177, or JNJ-87189401
Participants with leptomeningeal disease or brain metastases, with the exception of participants with definitively, locally treated brain metastases that are clinically stable and asymptomatic greater than (>) 2 weeks, and who are off corticosteroid treatment for at least 2 weeks prior to first dose of study treatment
Any T-cell redirecting treatment (e.g., CD3-directed bispecific or Chimeric Antigen Receptor T-cell [CAR-T] therapy) within 90 days prior to the first dose of study treatment
Sequential
JNJ-78278343
DrugJNJ-78278343 will be administered intravenously.
JNJ-95298177
DrugJNJ-95298177 will be administered intravenously.
JNJ-87189401
DrugJNJ-87189401 will be administered.
Number of Participants With Adverse Events (AEs) by Severity
An AE is any untoward medical occurrence in a participant participating in a clinical study that does not necessarily have a causal relationship with the pharmaceutical/biological agent under study. Severity will be graded according to the National Cancer Institute Common Terminology Criteria for Adverse Events (NCI-CTCAE) version 5.0. Severity scale ranges from Grade 1 (Mild) to Grade 5 (Death). Grade 1= Mild, Grade 2= Moderate, Grade 3= Severe, Grade 4= Life-threatening and Grade 5= Death related to adverse event. Cytokine release syndrome (CRS) and immune effector cell associated neurotoxicity syndrome (ICANS) will be graded according to the American Society for Transplantation and Cellular Therapy (ASTCT) guidelines and ocular events will be graded using the alternative scale provided in the protocol.
Part 1: Number of Participants With Dose-Limiting Toxicity (DLT)
High grade hematologic or non-hematologic toxicities with exceptions and/or toxicities leading to treatment discontinuation will be regarded as DLT.
Objective Response Rate (ORR)
ORR is defined as the percentage of participants who have a partial response (PR) or better according to the response evaluation criteria in solid tumors (RECIST) version 1.1 response criteria without evidence of bone progression according to prostate cancer working group 3 (PCWG3).
Prostate-Specific Antigen (PSA) Response Rate
PSA response rate is defined as the percentage of participants with a decline of PSA of 50% or more from baseline.
Radiographic Progression-Free Survival (rPFS)
rPFS is defined as the time from the date of first dose of any study treatment until the date of radiographic disease progression or death, whichever comes first.
Time to Response (TTR)
TTR is defined for the responders as the time from the date of first dose of any study treatment to the date of first documented response.
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