  Despite being of fundamental importance and potential interest for
topological quantum computing, spin-triplet superconductors remain rare in
solid state materials after decades of research. In this work, we present a
general mechanism for spin-triplet superconductivity arising from excitonic
effects in multi-band systems, where non-retarded pairing interaction is
produced from the electron-electron repulsion itself through virtual inter-band
transitions. Our theory is analytically controlled by a strong-coupling
expansion in the kinetic energy term and explicitly demonstrated in doped band
insulators with the example of an extended Hubbard model. In light of this
theory, we predict that the recently discovered superconducting WTe$_2$ is
spin-triplet and compare the expected consequences with experimental data.
