  The states generated by a multiport beam-splitter usually display genuine
multipartite entanglement between the many spatial modes. Here we investigate
the different classes of multipartite entangled states that arise in this
practical situation, working within the paradigm of Stochastic Local Operations
with Classical Communication. We highlight three scenarios, one where the
multipartite entanglement classes follow a total number hierarchy, another
where the various classes follow a nonclassicality degree hierarchy and a third
one that is a combination of the previous two. Moreover, the multipartite
entanglement of higher-dimensional versions of Dicke states relate naturally to
our results.
