The dynamics of Fierz-complete four-quark interactions and its influence on the QCD phase diagram have been investigated within the functional renormalization group approach to QCD at finite temperature and densities. It is found that in the vacuum the pion and sigma channels play the overwhelmingly dominant role, and all the other channels are negligible. However, when it is near the critical end point (CEP), the magnitude of four-quark couplings in other channels increases sizably and they become more and more important. In comparison to the single scalar-pseudoscalar channel of four-quark interactions, the dynamics of Fierz-complete four-quark interactions increases a bit the curvature of the phase boundary, and moves the CEP to location of larger baryon chemical potential and smaller temperature.