Specific language impairment (SLI) is a heterogeneous disorder affecting various aspects of language. While most studies have investigated impairments in the domain of syntax and morphosyntax, little is known about compositional semantics and the process of deriving pragmatic meanings in SLI. We selected a group of sixteen monolingual Italian-speaking children with SLI (mean-age 7;4) with a severe morphosyntactic deficit at the receptive and expressive level. We tested their comprehension of quantified sentences including all and some in order to establish whether they were competent with the logical and pragmatic meanings of these quantifiers. Children performed as well as their typically developing controls in understanding logical meanings. In comprehending pragmatic meanings, they obtained lower scores than age-matched controls but they were not different from language-matched children. However, differences in this ability correlated positively with age and with the ability to understand simple sentences in the SLI group. This suggests that aspects of the syntactic component might be involved in the development of this ability and that, despite their severe morphosyntactic deficits, children with SLI might catch up with their peers in deriving pragmatic meanings.