A general class of exactly soluble three-level models is presented for an
N-fermion system. Assuming a monopole-monopole interaction among the fermions allows one to express the model Hamiltonian in terms of the generators of the
SU3 group. A specialized version of this class of models is adapted for the study of mixing two collective states of opposite parity, analogous to the mixing of giant-dipole-resonance and surface quadrupole vibrations in nuclei. Exact results of the model are studied as a function of interaction parameters and compared with approximations including up to three-particle-three-hole excitations. It is shown that in the model many-particle-many-hole states play an important role in the mixing of collective states and cannot be properly neglected. The implications of this result for the study of actual nuclei is discussed.