The paper discusses the construction of new modified theories of gravity using a canonical formulation that allows for fundamental fields distinct from the emergent space-time metric. This approach avoids the usual uniqueness theorems by introducing a novel ingredient, allowing for fundamental fields of gravity that are not the emergent space-time metric. The authors demonstrate this by constructing new theories in a spherically symmetric setting, which can include expansion-shear couplings in cosmological models and modified Newtonian dynamics (MOND) without introducing extra fields. These theories help to make effective models of canonical quantum gravity fully consistent with general covariance. The key idea is that the space-time metric is emergent and not fundamental, and the emergent metric is determined by the structure function of the Poisson bracket of Hamiltonian constraints. This allows for new types of dynamical signature change and non-singular black hole solutions. The paper also explores the implications of these theories for cosmological models and intermediate-strength gravity, highlighting new physical effects such as expansion-shear couplings and modifications to MOND.The paper discusses the construction of new modified theories of gravity using a canonical formulation that allows for fundamental fields distinct from the emergent space-time metric. This approach avoids the usual uniqueness theorems by introducing a novel ingredient, allowing for fundamental fields of gravity that are not the emergent space-time metric. The authors demonstrate this by constructing new theories in a spherically symmetric setting, which can include expansion-shear couplings in cosmological models and modified Newtonian dynamics (MOND) without introducing extra fields. These theories help to make effective models of canonical quantum gravity fully consistent with general covariance. The key idea is that the space-time metric is emergent and not fundamental, and the emergent metric is determined by the structure function of the Poisson bracket of Hamiltonian constraints. This allows for new types of dynamical signature change and non-singular black hole solutions. The paper also explores the implications of these theories for cosmological models and intermediate-strength gravity, highlighting new physical effects such as expansion-shear couplings and modifications to MOND.