In this paper we will provide a description of what we term here the Coreferential Dative Construction. The languages under consideration are Syrian Arabic, which has never been studied before from this respect, and Modern Hebrew. We will show that this construction, related to other constructions containing non-selected datives, expresses the speaker's stance or emotional attitude towards the described eventuality by seeing it as having weak relevance. We will also show that the most important grammatical difference between the two languages is that in Syrian Arabic the presence of the Coreferential Dative obligatorily triggers a special type of modification in the VP: it must be modified by an attenuative vague measure. The comparative approach will help to shed new light on previous analyses of Modern Hebrew data.