At first blush this seems likely to introduce more (and more subtle) errors than it's worth. It requires that all of the various method bodies be written in such a way that they not step on one another's toes, but this is exactly opposite the usual concern when people write multiple versions of the same method; namely, to override functionality present at higher levels in the hierarchy!
The one place I can see using this is in initializer methods which are (often) meant to be called in sequence all the way up the tree. (Cf. inheritance: constructors). However NEXT already does just this.