The system would be described by a multi-particle state, which would be reducible. Of course, Wigner's classification is just for classifying (most) elementary

The system would be described by a multi-particle state, which would be reducible. Of course, Wigner's classification is just for classifying (most) elementary particles. A hydrogen atom can be considered a particle in some contexts, as can waves of spin in a magnet; I am specifically talking about elementary particles!