 The thrust of these no-go results is that straightforward constructions of plausible models for composite systems destroy regularity conditions (ortho-coherence in the case of the Foulis-Randall result, orthomodularity and the covering law in that of Aerts’ result) that have widely been used to underwrite reconstructions of the usual quantum-mechanical formalism. This puts in doubt whether any of these conditions can be regarded as having the universality that the most optimistic version of Mackey’s programme asks for. Of course, this does not rule out the possibility that these conditions may yet be motivated in the case of especially simple physical systems.