snap knife cut points to elements that aren't part of selection

I’m trying to make a knife cut using elements that aren’t part of the selection as snapping references (i.e. without cutting the reference elements). Possible?

You probably want to use knife project and create a cutting object whose geometry is snapped to the objects you want to use as a guide. Shift K will only cut selected faces but will not let you snap to anything that’s not selected, so it’s not likely to be much help.

Okay… but is there any way to do this solely in edit mode (without involving other objects)? That would remove many unnecessary steps. I assume the answer is no, but I’ll ask to be sure.

edit: I also want the cut to only affect selected faces.