We develop a nonlinear thermodynamic model for multilayer ferroelectric heterostructures that takes into account electrostatic and electromechanical interactions between layers. We concentrate on the effect of relative layer fractions and in-plane thermal stresses on dielectric properties of Ba0.6Sr0.4TiO3-, BaTiO3-, and PbZr0.2Ti0.8O3 (PZT)-SrTiO3 (STO) multilayers on Si and c-sapphire. We show that dielectric properties of such multilayers can be significantly enhanced by tailoring the growth/processing temperature and the STO layer fraction. Our computations show that large tunabilities (∼90% at 400 kV/cm) are possible in carefully designed barium strontium titanate-STO and PZT-STO even on Si for which there exist substantially large in-plane strains.