How many traits can one pet have?

[PuffyAmi]

In CAP I gave my dog the usual amount of 3 traits. During the gameplay the dog keeps getting more traits, "trained traits" and so far the dog has about 7 traits already. Will this List not end?
Unless it's just a glitch.

[Zokugai]

I don't believe there's necessarily a max limit as long as you keep training them. As you've probably noticed, it generated a scrollbar.