 In (35), with the possessive presupposition trigger “their cars”, there is a global context (outside of the scope of “most”), a local context corresponding to the scope of the quantifier (occupied by the VP “wash their cars on Saturday”), and also an intermediate context in the restrictor of the quantifier (occupied by “Germans”). The most natural interpretation of this sentence surely is that most Germans who own a car wash it on Saturday. So in this case intermediate accommodation seems to be the preferred option, and this might be explained, following van der Sandt (1992), by supposing that the possessive pronoun contains a variable bound by the quantifier.