Currently, I ride with a thin dressage pad and a sheepskin half pad (Mattes dressage). Specialized may suggest that you shouldn't use thick pads, but I've found if you don't add padding your horse will come up sore on long rides. Mine did when I used a correctly fitted specialized and a thin dressage pad.
If you use a thicker pad, you may have to adjust your saddle's width a little. But honestly I got mine fitted to my horse's bare back and added the sheepskin after several sore rides without any adjustment.
Heck, my horse never comes up sore anymore.
Riding with two pads is pretty annoying though, especially if you need to tack up quick. I'm saving up for an equipedic or skito pad, which provides padding without the bulk.
Several of my friends have used those combos with their specialized with good results.