Is it possible to cut out the wallboard where the bathroom mirrors are and build in a medicine cabinet framed with 2x4's and then reattach the mirror with the added support of say 3/8 inch plywood backing and molding to make it look good. Attached with some reasonable heavy duty hinges? Or would it be to heavy and collapse the wall.

Or do you know of a better solution that would create medicine cabinets for me in both bathrooms. The under sink cabinet just isn't enough.