I've had my Cayenne Turbo for about 6 years now. About half that time has been on the 32s(265/65/18).
These are the tires used on the Transsyberia race Cayennes.
I'm not sure I'd really want to go much bigger. The beauty of the Cayenne is that it does EVERYTHING, and does it FREAKISHLY WELL!! Tows awesome, drives like a real sports car, goes like a super car, and 4 wheels.
By going to bigger tires and messing with the suspension you start to change it into "just another lifted SUV". Sure, it would have more power, but it wouldn't really be any different or better than a Touareg at that point. The off road tires become the limiting factor VERY quickly for cornering, braking and acceleration.
Putting the power aside the real advantages to the Cayenne is the handling, the 66/33 torque split in the tcase, etc.
If you want a true crawler of a 4x4 you may as well start with the Touareg and its 50/50 tcase.
There are definitely days when I wish I were still on the smaller, stickier stock type tires. The BFGs take all the handling fun out of the Cayenne since they are the limiting factor. Just pushes in corners now, lights up all four tires instead of accelerating, and doesn't brake as well.
I've built several crawlers on 37s over 25 years of wheeling. I can't think of any place I would *reasonably* go with a Cayenne that would need anything bigger than 32s. Good driving skills can take you almost anywhere.
Here is mine again as a refresher.