  A mean field analysis of finite density QCD is presented including the
effects of additional chiral invariant four-fermion interactions. A lattice
regularization is used with N_f=4 flavors of staggered fermions. The use of the
four-fermion coupling as an improved extrapolation parameter over the bare
quark mass in Monte Carlo simulations is discussed. Particular attention is
given to the structure of the phase diagram and the order of the chiral phase
transition. At zero gauge coupling, the model reduces to a Nambu-Jona-Lasinio
model. In this limit the chiral phase transition is found to be second-order
near the zero-density critical point and otherwise first-order. In the strong
gauge coupling limit a first-order chiral phase transition is found. In this
limit the additional four-fermion interactions do not qualitatively change the
physics. The results agree with previous studies of QCD as the four-fermion
coupling vanishes.
