I am +0.3 on this as I don't personally have a need for this but do see the utility.
I can think of a number of examples where an `__advance__` would be preferable to any of the proposed solutions:
A skip list which doesn't support O(1) random access but can advance faster than naively calling next repeatedly
A lazy infinite iterator which can efficiently calculate its state at some future point (e.g. `itertools.count`)
A tree iterator could perform efficient `__advance__` by checking the size of sub trees before descending into them (I'm not sure why you would ever want to `__advance__` a tree iterator).
My ladder two examples demonstrate that this could have utility outside of sequences but for iterators in general.
-- Caleb Donovick