The Dig rule states (i.e., when rolling it on the Treehouse die):
Dig: You may move as many of your pieces as you wish to the tops of the towers they are in.
And the Movement rule states:
... a piece may "dig" to the top of the stack it's in by spending the Movement Points needed to move that piece one space.
It doesn't say "per layer" on either - it says "to the top."