optics - Is there any physical reason a mirror lens could not have a variable aperture?

I understand that mirror lenses already have high maximum apertures and that often, the last thing one wants to do is let in less light, but is there a physical reason that one could not build a working mirror lens that did use a variable aperture? Is it impossible to put the aperture in the right place? Is there something about the optical pathway that would ruin the functionality of an aperture. The advantage would be that one could get greater depth of field.