  An extensive generalization of the ordinary and quasi-eikonal methods is
presented for the $pp$ and $\bar pp$ elastic scattering amplitudes, which takes
into account in a phenomenological way all intermediate multiparticle states
involving the crossing even and crossing odd combinations of Reggeons. The
formalism in this version involves a maximum of three parameters corresponding
to the intermediate states which are possible in this configuration. The
unitarity restriction is investigated and particular cases are discussed. An
interesting result that emerges concerns the Odderon trajectory intercept: we
find that unitarity dictates that this quantity {\it must} be below or equal
unity unless a very peculiar equality exists between the coupling of the
particles to the Pomeron and the Odderon.
