Can an Overlay mode access existing tokens?

Basically I’d like to write an overlay mode that takes advantage of the previous mode’s parsing. In other words, imagine stream but returning tokens instead of chars. That way I can say if this is a token of this type that follows a token of this type, then return “blah”.

No, but you can do this if you directly/manually wrap a mode, rather than using the overlay addon.

Are there any examples of manually wrapping a mode?

Maybe this one: