The way they ended up implementing companions it's not exactly like you're "slotting" X companion permanently the same way you have an active mount or pet.
The companion can be dismissed automatically by the game at any time when you log in after all. Based on zone population and whatever.
I dont think it would work. The pet and mount are both chosen. The compagnion on the other hand works more like a memento that you use on will. That makes it hard for the game to decide which one should be used.