  We prove some new evaluations for multiple polylogarithms of arbitrary depth.
The simplest of our results is a multiple zeta evaluation one order of
complexity beyond the well-known Broadhurst-Zagier formula. Other results we
provide settle three of the remaining outstanding conjectures of Borwein,
Bradley, and Broadhurst. A complete treatment of a certain arbitrary depth
class of periodic alternating unit Euler sums is also given.
