Ply always needs to run across the joists, or you lose a lot of strength. Since you already have about 1" or so of subfloor, the new stuff is not for strength, I'd just screw it down, but across the joists to gain maximum benefit anyways.
If the glued top layer is something like partical board, you are asking for big troubles with tile, since the stuff swells at the hint of moisture. Since it is glued, you might have to take all of it out to the joists. If it is plywood, you're good to go for the floor raising with another layer.
While more money, you might want to consider adding self-leveing-cement. You could do that in one layer, and not need cbu, and not add more ply. You could use a membrane on top of it like Ditra, but it would not be required. This has good and bad points...the slc will level the floor. Depending on the actual floor, it might be quite thick in some areas, and could cause problems with the transition through the door. But, it gives a really nice tileable surface, quickly. You would need it to be at least 3/8" thick or so across the whole floor to cover the required lath on a wood subfloor and have a good surface.