I've seen somewhere a clever trick that derives some QM with a small tweak in GR. I can't judge whether the trick makes sense, though. So the trick was to modify the ds2=c2dt2-dx2-dy2-dz2 equation to exp(a cos(wt))ds2=... That extra exp(...) modulation, when combined with Lorentz transforms, produced some basic QM formula. With more wizardry, the author derived the time-dependent Schrodinger equation. Someone who knows GR well could probably tell if GR has "room" for the exp(...) modulation, i.e. that something in GR doesn't fall apart after this addition.