In this paper, we investigate a new way to deal with the problems generated by the limitation process of very high-order finite volume methods based on polyno- mial reconstructions. Multi-dimensional Optimal Order Detection (MOOD) breaks away from classical limitations employed in MUSCL or ENO/WENO. Indeed, instead of classical limiting of polynomial reconstructions, MOOD detects problematic situations after each time evaluation of the solution. Then, locally, the flux approximations are modified by reducing the local polynomial degree and the solution is updated. Several advantages are consequently gained: the concept is simple, totally independent of mesh structure in any spatial dimension and is able to take physics into account thanks to its “a posteriori” detection. The detection uses the Discrete Maximum Principle (DMP) for advection problem. For Euler system the detection is based on a mix between DMP on density variable and positivity of pressure. In order to avoid expensive substeps of polynomial limiting the solution re-evaluations are embedded into the substeps of a Runge-Kutta high-order time discretization. Numerical results on classical and demanding tests cases are proposed on quadrangular meshes to support the promising potential of this approach.