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In this paper we describe a reformulation strategy for solving multidimensional Constraint Satisfaction Problems (CSPs). This strategy operates by iteratively considering, in isolation, each one of the uni-dimensional constraints in the problem, and exploits the approximate symmetries induced by the selected constraint on the domains in order to enforce this constraint on the simplified problem. We use the game of SET, a combinatorial card game, as a toy problem to motivate our strategy and to explain and illustrate its operation. However, we believe that our approach is applicable to more complex domains of scientific and industrial importance, and deserves more thorough investigations in the future. Our approach sheds a new light on the dynamic reformulation of multidimensional CSPs. Importantly, it advocates that modeling tools for Constraint Programming should allow the user to specify the constraints directly on the attributes of the domain objects (i.e., variables and values) so that their multi-dimensionality can be exploited during problem solving.