So far as I'm aware I've yet to see any sort of food limit per counter in all my years of playing. As you've noticed, similar food gets piled together when you run out of empty counters but that's about it so far as counter rules go. When you see multiple counters with the same recipe on it, that just means that the player has placed extra counters out.
They would do this either for future food placement or to ensure that the food sells quicker, as many theorize that food sells faster when the amounts per counter are lower. Personally, I go for more counters simply because I redecorate often and do not want to wait around for the food to sell or waste the food by storing a full counter.