If you look here,
www.seatexboards.com/carbon-deep-tuttle-fin-box-v-2-on-sale/or google "deep tuttle finbox" and look at the pictures, you will see that there is a lot of variation in wall thickness. In general, those with thicker walls, and/or extra reinforcements, are foil ready.
The custom foil board builder I know in Hood River uses a thick-walled reinforced deep tuttle finbox for all their foil boards, without exception. (They even add 16" long stringers running forward to add strength for the cantilevering forces exerted by foils.) What they do is cut off the top of the box so that there is no roof, but there is a gap between the inside of the top of the box and the bottom of the top deck of the board. The top deck of the board is greatly reinforced with extra carbon and glass to carry the loads of the fender washers on the fin screws. They do not make screw tunnels like you see on some boards. They consider such tunnels anathema. Cheap and weak.
When I bought a foilboard from them last year, they made a HUGE point of this thing about leaving a gap between the top of the foil fitting and the inside bottom of the board's top skin. They emphasized that you MUST get a tight locking fit to the tapers, and nowhere else. (Parallel sides, of course, too.)
With the gap it is possible to fit different foils to the same box since all foils (and fins, too) have various fitting heights. AFS and Moses, for example, have really tall fitting heights, while LP and Power Box, for example, have a shorter height. They all fit perfectly since they all lock to the tapers and stop there, with whatever gap is remaining. All of this is true, also, for formula fins.