  Using a BRST treatment, we show that the equivalence of General Relativity
and Shape Dynamics can be extended to a theory that respects the
BRST-symmetries of General Relativity as well as the ones of an extended
version of Shape Dynamics. This version of Shape Dynamics implements local
spatial Weyl transformations as well as a local and abstract analogue of
special conformal transformations. Standard effective field theory arguments
suggest that the definition of a gravity theory should implement this duality
between General Relativity and Shape Dynamics, thus the name "Doubly General
Relativity." We briefly discuss several consequences: bulk/bulk- duality in
classical gravity, experimental falsification of Doubly General Relativity and
possible implications for the renormalization of quantum gravity in the
effective field theory framework.
