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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, thedoi:10.1103/physrevd.56.5596 fatcat:q3c3ddkdzvctdbekfqiqt2inda