I think every single character can join your party when you reach a certain amount of friendship with them. The higher the friendship, the longer they will stay in your party and eventually they won't leave your party unless you ask them to leave.
While most do there are a few exceptions actually, Granny Blossom being one either because of her age or poor health. Though you can sprite swap to fight as her iirc, but I know that's not the same.