Short answer is yes, it can spread in a minority of men without the expected rise in PSA. We have had (a very few) members on this forum who have experienced ithis. A widely respected Mayo oncologist said he had experienced rare cases where the cancer had spread when the PSA was zero. I won't post the link again unless requested, as it has been posted several times previously.
It could help identify the present situation if you had a PSMA scan, but where the cancer has spread more widely and extensively, regardless of the result and what you have previously told us, it is likely that further treatment would be systemic.