In this paper, we propose to put together the intuition developed in the descriptive work by Cusic on plurality in the verbal domain and the formal tools developed by Landman on groups. Cusic's hierarchy is used to say something both on the accessibility of the members of a plurality, and on the iteration of pluralisation to produce predefined new units. The notion of structured unit such as a group introduces a breaking point in the transitive relation that is part of the definition of the partial order imposed on the denotation of a predicate. Looking inside a group means to jump out of the semilattice to which the group belongs, and to land into another semilattice generated by a set of elements that are units (or collections thereof) of a different layer and are associated with a different sub-sortal. Discourse accessibility of the elements in the landing structure is not warranted.