So there is no possible way to have max stats? So how far do some of the stats even go?
No, because a) a Pokemon can only have one Nature, and every nature gives a boost to one stat while dropping another or does nothing at all, and b) you can only give a Pokemon 510 EVs at a time, but 255 to any given stat. It's impossible to max all stats at once.
And if you mean "stat cap", it's impossible to max one stat. Whatever the stat cap is, it's higher than the actual maximum possible stat (which would be Blissey with max HP (714), or Shuckle with max Defense or Special Defense (614) for a more traditional stat.)
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