This work presents a simulation study of a ferroelectric field effect transistor (FeFET), which leverages a metal interlayer to achieve a multilevel operation thanks to the interplay between the ferroelectric polarization and the charge stored in the interlayer. We show that the metal interlayer can effectively stabilize the ferroelectric polarization even for a negligible charge trapping in the dielectric stack and, moreover, enable a multilevel operation even for a uniform ferroelectric polarization.