• Implicature consists in a series of sub-computations, but these can be computed online or stored. • Evidence from priming suggests the quantifier some and number words involve a shared computation. • The most likely candidate for this shared computation is the negation of alternatives. • Alternatives for number are lexically stored, but the alternatives for some are computed online. • Free Choice disjunctions do not show evidence for a shared computation with either some or number. Across a wide variety of semantically ambiguous sentences, implicature has been proposed as a single mechanism which can derive one reading from another in a systematic way. While a single formal mechanism for computing implicatures across disparate cases has an appealing parsimony, differences in behavioral and processing signatures between cases have created a debate about whether the same computation really is so widely shared. Building on previous work by Bott and Chemla (2016), three experiments use structural priming to test for shared computations across three purported cases of implicature: the quantifier some , number words, and Free Choice disjunctions. While we find evidence of a shared computation between the enriched readings of some and number words, we find no evidence that Free Choice readings involve any shared computation with either some or number. Along with evidence of a shared mechanism between some and number implicatures, we also find substantial differences between these two cases. We propose a way to reconcile these findings, as well as seemingly contradictory prior evidence, by understanding implicature as a sequence of separable sub-computations. This implies a spectrum of possibilities for which sub-computations might be shared or distinct between cases, instead of a single implicature mechanism that can only be either present or absent. [ABSTRACT FROM AUTHOR]