In order to bring the diverse functionalities of transition metal oxides into modern electronics, it is imperative to integrate oxide films with controllable properties onto the silicon platform. Here, we present asymmetric LaMnO3/BaTiO3/SrTiO3 superlattices fabricated on silicon with layer thickness control at the unit-cell level. By harnessing the coherent strain between the constituent layers, we overcome the biaxial thermal tension from silicon and stabilize c-axis oriented BaTiO3 layers with substantially enhanced tetragonality, as revealed by atomically resolved scanning transmission electron microscopy. Optical second harmonic generation measurements signify a predominant out-of-plane polarized state with strongly enhanced net polarization in the tricolor superlattices, as compared to the BaTiO3 single film and conventional BaTiO3/SrTiO3 superlattice grown on silicon. Meanwhile, this coherent strain in turn suppresses the magnetism of LaMnO3 as the thickness of BaTiO3 increases. Our study raises the prospect of designing artificial oxide superlattices on silicon with tailored functionalities.