I am prepping the living room in my house for a pre-finished Brazilian Cherry install. The foyer, which will butt up to the hardwood, is ceramic tile on a radiant heat mudbed. Very thick. Right now, the living room floor is the original 1x6 on the floor joists and is about 2-7/8 below the top of the ceramic. I would like to build up the living room floor with multiple layers of plywood so that the floor will be even when completed. Other than the obvious staggering and crossing the layers, is there any other advise that anyone can give? Should they all be nailed down, screwed down, glued down etc.? Any help would be appreciated.