2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/130516We 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.21 pages, To appear in Compositio MathematicaClassical Analysis and ODEsNumber Theory33E20 (Primary) 33C05, 11G55 (Secondary)text