In this paper, we discuss so-called 'de re' attitude reports (i.e. reports that contain at least one referential term inside the clausal complement of an attitude verb). Common treatments of such reports follow the lines of Kaplan (1968) and assume that there is a unique guise under which the 'res' (the object) denoted by the referential term is given to the attitude holder in the described situation. Technically speaking, attitude verbs are believed to introduce existential quantification over acquaintance relations or concepts above the universal quantification over possible worlds. We argue that there are cases that cannot be captured by Kaplanian accounts. We construct a case of a 'de re' report about a disjunctive desire. Its truth conditions can be correctly predicted only by a system in which guises are allowed to vary from one desire-alternative to another. We build on a particular version of a 'de re' account, namely, the theory of concept generators (Percus and Sauerland 2003). We propose a modified version of this theory where, instead of variables over concept generators, variables over generators of concept sets are used. Such generators are functions that take an individual and generate all possible concepts of this individual for the attitude holder. In different desire-alternatives, different concepts can be picked from this set. The job of picking is done by choice functions, variables over which are merged in the syntax. Those variables can be existentially closed at any sentential level. We demonstrate that the revised theory also has a technical advantage over the more standard approaches. It allows us to dispense with type-flexibility of attitude predicates that has been assumed for cases like "John thinks that Clark Kent is not Superman", where one 'res' is referred to with different terms.