  We construct extensions of the standard model based on the hypothesis that
the Higgs bosons also exhibit a family structure, and that the flavor weak
eigenstates in the three families are distinguished by a discrete $Z_6$ chiral
symmetry that is spontaneously broken by the Higgs sector. We study in detail
at the tree level models with three Higgs doublets, and with six Higgs doublets
comprising two weakly coupled sets of three. In a leading approximation of
$S_3$ cyclic permutation symmetry the three Higgs model gives a ``democratic''
mass matrix of rank one, while the six Higgs model gives either a rank one mass
matrix, or in the case when it spontaneously violates CP, a rank two mass
matrix corresponding to nonzero second family masses. In both models, the CKM
matrix is exactly unity in leading approximation. Allowing small explicit
violations of cyclic permutation symmetry generates small first family masses
in the six Higgs model, and first and second family masses in the three Higgs
model, and gives a non-trivial CKM matrix in which the mixings of the first and
second family quarks are naturally larger than mixings involving the third
family. Complete numerical fits are given for both models, flavor changing
neutral current constraints are discussed in detail, and the issues of
unification of couplings and neutrino masses are addressed. On a technical
level, our analysis uses the theory of circulant and retrocirculant matrices,
the relevant parts of which are reviewed.
