The foundations of Many-Fermion Dynamics (MFD) are developed with special attention paid to a treatment of color and flavor degrees of freedom. From these ingredients a framework was developed to calculate the properties of many-fermion bound states. The quark implementation of MFD (MFDq) was extensively tested on the 2-body problem against the established nucleon implementation of MFD (MFDn). We were able to perform a limited set of self-consistency checks of MFDq in the 4-body problem to test a proper treatment of all computed matrix elements.;Finally, calculations are presented using MFDn to predict the properties of 4-body charmonium bound states. With MFDn, we did find a lowest bound state of J = 0 at 6.033 GeV with a deviation of .084 GeV. Additional bound states are also obtained. Preliminary calculations with MFDq qualitatively confirm these results.