Plural phrases are open to many interpretations in English, where cumulative interpretations of noun and verb phrases are possible without any disambiguating morphology. A sentence like Every week, the high school kids went to the movies or the ballgame might involve quantifying over multiple occurrences of a single scenario, in which subsets of the kids do different things, or it might involve quantifying over distinct scenarios, in which all of the kids do one thing or all of them do the other. In the present work and related earlier work (Harris et al., 2013), we pursue the No Extra Times principle that favors interpretations where a phrase is construed as describing a single event taking place during a given time period. In two written interpretation studies, we found that participants more often interpret indeterminate sentences with disjunctive predicates by partitioning the set of individuals rather than partitioning the predicate to denote distinct scenarios or times. We conclude by offering some speculations about why partitioning the eventuality denoted by the verb phrase into multiple times is more costly than partitioning the entities denoted by its subject noun phrase into multiple sets.