 The most natural interpretation of B’s answer, in this context, is that it is possible that the stranger has a girlfriend who has jilted him; this construal will require local accommodation of the girlfriend if we assume that “his girlfriend” always triggers the presupposition that the pronoun’s referent has a  girlfriend.[23]  The problem is that if this is local accommodation, then it’s too easy. Local accommodation is supposed to be dispreferred. If we allow that in this case the presupposition is locally accommodated, why can’t all embedded presuppositions just be locally accommodated away and not project? Allowing local accommodation to occur without constraint would potentially destroy any claim to have explained the observation that has defined the phenomenon of presupposition since its inception, the observation that presuppositions tend to project.