Luffy accidentally ate the Gomu-Gomu (Rubber-Rubber) fruit, but was interrupted by Shanks after a few bites. It was too late and Luffy got the Devil's Fruit powers anyway. If he had instead eaten the whole of it, would he have got even more power from the fruit?
In the One Piece wiki, it's stated, that it doesn't matter, how much someone eats.
Only one bite is needed for the user to gain the power of a Devil Fruit, after which the Devil Fruit becomes a simple, useless, disgusting fruit. Swallowing the fruit whole, as Buggy did, has the same effect, as well as peeling off the skin and eating it piece by piece also works.
However, that is never stated in the manga/anime.