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In this paper, we investigate the dynamics of solutions of the Muskatequation with initial interface consisting of multiple corners allowing forlinear growth at infinity. Specifically, we prove that if the initial datacontains a finite set of small corners then we can find a precise descriptionof the solution showing how these corners desingularize and move at the sametime.  At the analytical level, we are solving a small data critical problem whichrequires renormalization. This is accomplished using a nonlinear change ofvariables which serves as a logarithmic correction and accurately describes themotion of the corners during the evolution.

Desingularization of small moving corners for the Muskat equation