Study of JANX007 in Subjects With Metastatic Castration-Resistant Prostate Cancer (ENGAGER-PSMA-01)

Inclusion Criteria: * Male ≥18 years of age at the time of signing informed consent * Histologically or cytologically confirmed adenocarcinoma of the prostate * For Dose Escalation and Backfill: Having mCRPC that progressed after at least one novel anti-androgen therapy and at least one taxane containing regimen. Participants who have actively refused a taxane containing regimen or are medically unsuitable to receive taxane are eligible * Adequate organ function * For Monotherapy Expansion Part a: Have received ≤ 2 anti-androgen therapies in either the HSPC or CRPC setting and no more than 1 prior taxane regimen in the HSPC or CRPC setting. Participants who have actively refused a taxane regimen or are medically unsuitable to receive taxane are eligible. * For Monotherapy Expansion Part b: Have received ≤ 2 anti-androgen therapies in either the HSPC or CRPC settings * For Monotherapy Expansion Part d: Have received ≤ 1 anti-androgen therapy and a poly(ADP-ribose) polymerase (PARP) inhibitor for mCRPC and have progressed following treatment with the PARP inhibitor * For Combination Expansion: Have received ≤ 1 anti-androgen therapy other than darolutamide in the HSPC setting and ≤ 1 taxane in the mCRPC setting. Participants who have actively refused a taxane regimen or are medically unsuitable to receive taxane are eligible. Exclusion Criteria: * Prior solid organ transplant * Prior treatment with PSMA-targeted CAR-T cell therapy or PSMA-CD3, PSMA-CD28 or other CD3 T-cell engaging bispecific antibodies or radioligand therapy * Clinically significant cardiovascular disease * For Monotherapy Expansion Part a: Prior receipt of any treatment other than an ARPI or taxane in the mCRPC setting * For Monotherapy Expansion Part b: Prior receipt of any treatment other than an anti-androgen therapy or prior receipt of a taxane containing regimen or more than 1 prior line of therapy for mCRPC * For Monotherapy Part d: More than 1 prior line of therapy for mCRPC or prior receipt of any treatment other than an anti-androgen therapy and PARP inhibitor for mCRPC or prior receipt of a taxane in the mCRPC setting * For Combination expansion: More than 1 prior line of therapy for mCRPC or prior receipt of any treatment other than a taxane for mCRPC or prior receipt of Darolutamide or prior receipt of a taxane for HSPC * Active clinically significant infection (bacterial, viral, fungal, mycobacteria or other) * Any medical condition or clinical laboratory abnormality likely to interfere with assessment of safety or efficacy of study treatment