A post-quantum theory of classical gravity?

We consider a consistent theory of classical systems coupled to quantum ones. The dynamics is linear in the density matrix, completely positive and trace-preserving. We apply this to construct a theory of classical gravity coupled to quantum field theory. The theory doesn't suffer the pathologies of semi-classical gravity and reduces to Einstein's equations in the appropriate limit. The assumption that gravity is classical necessarily modifies the dynamical laws of quantum mechanics -- the theory must be fundamentally information destroying involving finite sized and stochastic jumps in space-time and in the quantum field. Nonetheless the quantum state of the system can remain pure conditioned on the classical degrees of freedom. The measurement postulate of quantum mechanics is not needed since the interaction of the quantum degrees of freedom with classical space-time necessarily causes collapse of the wave-function. The theory can be regarded as fundamental, or as an effective theory of quantum field theory in curved space where backreaction is consistently accounted for.