Yes, there can be max DVs. But there can't be max stats, at least not all six of them. Stats depend on species, level, DVs, EVs and Natures. All six DVs can be maxed out at the same time, but all six EVs can't; the most you can max at once is two. And, of course, the only Natures that don't lower a single stat by 10% are the ones that don't raise one by 10% either.
There's a code you can find at GameFAQs that will make the wild pokémon you encounter have max DVs; you can then catch and train them. Beyond that I don't know.