It has recently been pointed out that the mirror or twin Higgs model is more
technically natural than the standard model, thus alleviating the ``little''
hierarchy problem. In this paper we generalise the analysis to models with an
arbitrary number of isomorphic standard model sectors, and demonstrate that
technical naturalness increases with the number of additional sectors. We
consider two kinds of models. The first has N standard model sectors
symmetric under arbitrary permutations thereof. The second has p left-chiral
standard model sectors and p right-chiral or mirror standard model sectors,
with p-fold permutation symmetries within both and a discrete parity
transformation interchanging left and right. In both kinds of models the
lightest scalar has an invisible width fraction 1/N, which will provide an
important means of experimentally testing this class of models.Comment: about 8 page