  The majority of extensions to General Relativity display mathematical
pathologies (higher derivatives, character change in equations that can be
classified within PDE theory, and even unclassifiable ones) that cause severe
difficulties to study them, especially in dynamical regimes. We present here an
approach that enables their consistent treatment and extraction of physical
consequences. We illustrate this method in the context of single and merging
black holes in a highly challenging beyond GR theory.
