  We examine extensions of the MSSM with more than one generation of Higgs
bosons. If one assumes that a symmetry eliminates the tree-level FCNC, then the
extra scalar bosons do not acquire VEVs, do not couple to fermions and do not
mix with the ordinary Higgs bosons; the lightest is absolutely stable. The two
lightest neutral scalars, $\phi_S$, and $\phi_P$, are degenerate in mass, and
the mass difference between those and the lightest charged scalar, $\phi_+$, is
calculated. For most of the parameter space, the charged scalar is between a
hundred MeV and a few GeV heavier than the neutral scalars. The $\phi_+$ will
decay at the vertex; the signature for this decay will be like that of a
chargino with a nearly degenerate undetected neutralino. Next, the possibility
that the symmetry that eliminates FCNC is a flavor symmetry is discussed. In an
example, the U(2) model, tree-level FCNC processes can be calculated in terms
of quark masses. The strongest constraint on this model is from $D-\bar{D}$
mixing, which should be within an order of magnitude of the current bound.
