The Mandarin functional morpheme dou appears to have been interpreted, among other things, as a distributor, focus marker even, or already. This paper aims at providing a unified semantic account for these different uses. I argue that the semantic core of these different usages is the same: dou is simply a maximality operator. It gives rise to different meanings by applying maximality to a contextually determined plural set. This could be a set of covers, a set of focus-induced alternatives, or a set of degrees ordered on a scale. This analysis also connects dou in these contexts with dou in environments that license polarity items, as discussed in Giannakidou and Cheng (J Semant 23: 135–183, 2006).