In [1] it was shown that the automorphism groups of (1-)order expansions of several homogeneous structures with a stationary independence relation are simple. We follow the basic approach from [1] in order to show that the same holds true for n-order expansions, 1 < n. However, the passage from 1-orders to n-orders causes some extra challenge that requires a different proof idea. My proof involves a reduction of the problem to 1-orders that comes, in return, with significant constraints we have to deal with. [1] F. Calderoni, A. Kwiatkowska, K. Tent. Simplicity of the Automorphism Groups of Order and Tournament Expansions of Homogeneous Structures. Der Vortrag wird via Zoom übertragen. Für die Zugangsdaten setzen Sie sich bitte mit Dr. Bays in Verbindung: baysm@uni-muenster.de