  Doping ferroelectrics with carriers is often detrimental to polarization.
This makes the design and discovery of metals that undergo a ferroelectric-like
transition challenging. In this letter, we show from first principles that the
oxygen octahedral rotations in perovskites are often enhanced by electron
doping, and this can be used as a means to strengthen the structural
polarization in certain hybrid-improper ferroelectrics -- compounds in which
the polarization is not stabilized by the long range Coulomb interactions but
is instead induced by a trilinear coupling to octahedral rotations. We use this
design strategy to predict a cation ordered Ruddlesden-Popper compound that can
be driven into a metallic ferroelectric-like phase via electrolyte gating.
