  If the scalar sector of the Standard Model is non-minimal, one might expect
multiple generations of the hypercharge-1/2 scalar doublet analogous to the
generational structure of the fermions. In this work, we examine the structure
of a Higgs sector consisting of N Higgs doublets (where N \geq 2). It is
particularly convenient to work in the so-called charged Higgs basis, in which
the neutral Higgs vacuum expectation value resides entirely in the first Higgs
doublet, and the charged components of remaining N-1 Higgs doublets are
mass-eigenstate fields.
  We elucidate the interactions of the gauge bosons with the physical Higgs
scalars and the Goldstone bosons and show that they are determined by an Nx2N
matrix. This matrix depends on (N-1)(2N-1) real parameters that are associated
with the mixing of the neutral Higgs fields in the charged Higgs basis. Among
these parameters, N-1 are unphysical (and can be removed by rephasing the
physical charged Higgs fields), and the remaining 2(N-1)^2 parameters are
physical. We also demonstrate a particularly simple form for the cubic
interaction and some of the quartic interactions of the Goldstone bosons with
the physical Higgs scalars. These results are applied in the derivation of
Higgs coupling sum rules and tree-level unitarity bounds that restrict the size
of the quartic scalar couplings. In particular, new applications to three Higgs
doublet models with an order-4 CP symmetry and with a Z_3 symmetry,
respectively, are presented.
