[Ryuuku]

Actually we can only stable 3 pets, I think it is really low.
I think would be better if we could stable like 6/10 pets.

[Halo Dalgion]

Shrink pots should be around soon. Then wont even need stable.

[Shade]

Looked at the script, turns out you actually have a max of 5 stables. However this is dependent on pet related skills.
Basically if animal taming + animal lore + veterinary >= 240 you get 5 slots.