Intrinsic polar metals are rare, especially in oxides, because free electrons screen electric fields in a metal and eliminate the internal dipoles that are needed to break inversion symmetry. Here we use first-principles high-throughput structure screening to predict a new polar metal in bulk and thin film forms. After screening more than 1000 different crystal structures, we find that ordered BiPbTi 2 O 6 can crystallize in three polar and metallic structures, which can be transformed between via pressure or strain. In a heterostructure of layered BiPbTi 2 O 6 and PbTiO 3 , multiple states with different relative orientations of BiPbTi 2 O 6 polar displacements, and PbTiO 3 polarization, can be stabilized. At room temperature, the interfacial coupling enables electric fields to first switch PbTiO 3 polarization and subsequently drive 180°change of BiPbTi 2 O 6 polar displacements. At low temperatures, the heterostructure provides a tunable tunnelling barrier and might be used in multi-state memory devices.