i think you can but only one can be connected haha so basically you cant have both in your car at the same time
...the obivious stock intake... is considered a CAI. And you could 'drop in' an aftermarket 'drop in' filter like WORKS, K&N, etc. Sorry if this doesn't answer the question or help.
I'm sure something could be fabbed up to work with the stock box. If you throw in a performance filter, you could probably run some type of tubing from the inlet of the airbox to a location behind the bumper or behind the grille. If you do it that way, you could leave the piping open (I.e. No filter) because of the element in the airbox.
