We show that the electric polarization at the interface with ultrathin superconducting (S) films sandwiched between ferroelectric (FE) layers allows achievement of substantially stronger modulation of inner carrier density and superconducting transition temperature as compared to FE-S bilayers typically used in superconducting FET's. We find that not only the larger penetration depths but also the pairing symmetry should be responsible for the fact that the electric-field effect in high-temperature superconductors is much stronger than in conventional systems. Discussing the advantages of multilayers, we propose an interesting design concept for superconducting electric-field-effect transistors based on ferroelectric films.