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