It has been proposed that the part structures of denotations of plurals ‘project’ to the denotations of expressions including those plurals (e.g., Gawron & Kehler 2004, Kubota & Levine 2016, Schmitt 2019/2020). If such a plural projection is possible, not only plural DPs but also expressions including those plural DPs denote pluralities (e.g., saw the two recipes denotes a plurality {SAW(recipe1),SAW(recipe2)} instead of a singularity {SAW({recipe1,recipe2})}). One piece of support for plural projection comes from Schmitt’s (2020) observation about ‘non-local’ cumulativity. In this paper, I further examine when cumulativity is available non-locally, and show that a source of cumulativity in the literature (e.g., Krifka 1989, Kratzer 2007, Harada 2022b) can capture all the relevant non-local cumulativity data without plural projection while an analysis with plural projection can capture only a proper subset of those data. Therefore, this paper concludes that the relevant non-local cumulativity does not support the need of plural projection.