Geometrical Shock Dynamics (GSD) is a simplified model for nonlinear shock wave propagation for which the front evolution is governed by a local relation between the geometry of the shock and its velocity, so-called A − M rule. Numerous studies have proven the ability of the GSD model to estimate correctly the leading shock front in interaction with obstacles. Nevertheless, a solution for the problem of diffraction over a convex corner does not always exist, especially for weak shocks. To overcome this limitation, we propose an ad-hoc modification of the A−M relation for two-dimensional configurations: an extra term based on the transverse variation of the Mach number is added. This new closure is fitted against experimental observations, which ensures, by construction, a correct behaviour for expansive shocks. A Lagrangian numerical solver is developed, for which this new term is activated only on specific parts of the front. Results of this new model are compared with the original GSD model, experiments, and Eulerian simulations for several cases of increasing complexity. A noticeable improvement of the solution is observed.