Usual propositional possibilistic logic formulas are pairs made of a classical logic formula associated with a weight thought of as a lower bound of its necessity measure. In standard possibilistic logic, only conjunctions of such weighted formulas are allowed (a weighted classical conjunction is equivalent to the conjunction of its weighted conjuncts, due to the min-decomposability of necessity measures). However, the negation and the disjunction of possibilistic logic formulas make sense as well. They were briefly introduced by the authors some years ago, in a multiple agent logic context. The present paper hints at the multitiered logic that is thus generated, and discusses its semantics in terms of families of possibility distributions. Its practical interest for expressing higher order epistemic states is emphasized.