We calculate the classical limit effective action of the EPRL/FK  spinfoam model of quantum gravity coupled to matter fields. By  employing the standard QFT background field method adapted to the  spinfoam setting, we find that the model has many different classical  effective actions. Most notably, these include the ordinary  Einstein-Hilbert action coupled to matter, but also an action which  describes antigravity. All those multiple classical limits appear as a  consequence of the fact that the EPRL/FK vertex amplitude has  cosine-like large spin asymptotics. We discuss some possible ways to eliminate the unwanted classical limits.