ŝtuparo

This is -ar- doing what it always does: ŝtupo is one step, and the collective suffix gathers the steps into the thing they add up to, exactly as arbo becomes arbaro and vorto becomes vortaro. Once you see the pattern, half the vocabulary stops needing to be memorised. Note that ŝtuparo is singular where English insists on plural stairs, so any adjective agreeing with it stays singular too, and sur la ŝtuparo covers both "on the staircase" and "on the stairs". Ŝtupetaro is the ladder, a little staircase you can carry.