CJNJ-67652000 and Prednisone for Treatment of Metastatic Castration-Resistant Prostate Cancer and SPOP Gene Mutations

Inclusion Criteria: * Male \>= 18 years of age * Histological confirmation of adenocarcinoma of the prostate * Qualifying deleterious SPOP mutation detected on any archival genomic assay (tissue and/or liquid biopsy) is acceptable for study inclusion. Qualifying mutation(s) of SPOP include any genomic change predicted to be deleterious or suspected deleterious. SPOP status must be established prior to involvement on the trial * Evidence of metastatic castration-resistant prostate cancer, defined as at least one (1) documented metastatic lesion on either bone scan or CT scan. Bone only disease is acceptable for enrollment. Non-bone metastatic lesions must be measurable by Response Evaluation Criteria in Solid Tumors (RECIST) 1.1 criteria. Subjects whose disease spread is limited to regional pelvic lymph nodes or local recurrence (e.g. bladder, rectum) are not eligible * Radiographic or PSA progression while on androgen deprivation therapy (or after bilateral orchiectomy) AND at least one prior AR-targeted therapy (abiraterone acetate, enzalutamide, apalutamide, darolutamide or investigational AR-targeted agents). PSA progression is a PSA increase that is \>= 25% and \>= 2 ng/mL above the nadir, and which is confirmed by a second value (minimum 1 week interval between tests). For radiographic progression of soft tissue lesions, modified RECIST 1.1 criteria will be used to qualify entry. For radiographic progression of bony disease, two new lesions must be seen as per PCWG3 cri…