NOTE: Since I thought a presentation based on a handout would be more suitable for this online conference than a cluttered poster, there are both a poster and a handout, with exactly the same content. I also want to note that the system presented in the poster/handout differs in several ways from the sketch in the abstract, although the main ideas are preserved. This work connects two observations about cumulative readings: 1) a previously unnoticed contextual constraint on such readings that resembles constraints on non-maximality (Brisson 1998, Malamud 2012, Križ 2015 a.o.), and 2) their graded acceptability depending on how ‘close’ the cumulative scenario is to a distributive scenario (cf. Poortman 2016, Burnett 2017). I argue that plural sentences induce a scale based on an ordered partition of the logical space, with the cells for distributive scenarios at the top. These scales are computed via a nonstandard plural semantics where plurals denote higher-order scalar predicates. These predicates are a generalization of the `plural sets’ assumed by Schmitt (2019).