Right now, it's not possible to 'see' a pet when a character is mounted. This is not a problem, as you can simply dismount, to show the pet. I suspect, and it is true for me, that a mount which allows the pet to be seen would be a popular item. Perhaps a "pet platform" or basket, in which the creature rides. It might even be possible to allow the pet to travel alongside a mount, such as an equine, or feline variety. The chance to allow pet/mount interactions is not important, to me, but just to have a visible pet, while travelling about the spiral, would pry loose some of my crowns, or much of my gold. I wonder if this idea would appeal to others?
This is a novel idea. Perhaps a side car for the motorcycles. Your pet could be hanging out the window of any vehicle or riding behind you on a carpet.
It wouldn't have to EVERY mount, it could be just a select few. Much the same way that a select few or multi-rider mounts.