Left indexing radical — the numeral ten, here read as 'all together, full set.' Marks 协 in a small family of joining/totaling chars (协, 博, 千). The two crossed strokes evoke many things crossing paths, fitting the cooperative sense.
Right side 办 supplies a faded sound (bàn drifted to xié through tone and onset shift) and reinforces meaning — 'to manage / take care of.' Pairing ten with handling gives 'many hands jointly managing,' the core of 协作 (cooperate) and 协调 (coordinate).
