It has been argued that, despite remarkable success, existing random m
atrix theories are not adequate at describing disordered conductors in
the metallic regime, due to the presence of certain two-body interact
ions in the effective Hamiltonian for the eigenvalues, in addition to
the standard logarithmic interaction that arises entirely from symmetr
y considerations. We present a new method that allows exact solution o
f random matrix models with such additional two-body interactions. Thi
s should broaden the scope of random matrix models in general.