  For classic Lotka-Volterra systems governing many interacting species, we
establish an exclusion principle that rules out the existence of linearly
asymptotically stable steady states in subcommunitites of communities that
admit a stable state which is internally D-stable. This type of stability is
known to be ensured, e.g., by diagonal dominance or Volterra-Lyapunov stability
conditions. By consequence, the number of stable steady states of this type is
bounded by Sperner's lemma on anti-chains in a poset. The number of stable
steady states can nevertheless be very large if there are many groups of
species that strongly inhibit outsiders but have weak interactions among
themselves. By examples we also show that in general it is possible for a
stable community to contain a stable subcommunity consisting of a single
species. Thus a recent empirical finding to the contrary, in a study of random
competitive systems by Lischke and L\"offler (Theo. Pop. Biol. 115 (2017)
24--34), does not hold without qualification.
