You can more or less modify the player's movement metrics to be whatever you want, but it's a concern of whether or not the result is good. As far as I know, everything done in terms of movement is subject to the limitations of the tile grid, and I think that was already mentioned. If you're effectively moving two tiles ahead per keystroke, you'd have to be making collision checks for the 32x tile in front of you and the one two spaces away. It introduces a lot more variables for things that can go wrong and probably will look a little clunky moving a larger sprite in such a fashion.
I dislike that kind of modification that requires you to struggle against the engine though, so don't take my word for it!