Grammaticalization may entail a variety of non-essential mechanisms, such as schematization or lexicalization. What these processes have in common is a semantic expansion of the grammaticalizing form, translated empirically into a frequency increase following the so-called S-curve pattern. However, this pattern also holds in cases of semantic expansions within the lexical domain. As such, the specificity of grammaticalization does not lie in the unfolding of its process, but in the functional nature of the new meaning achieved through the semantic expansion. Existing attempts to quantify this functional dimension and to come up with a grammaticality score nonetheless still fail to offer a reliable solution to assess the specificity of grammaticalization on a quantitative basis.