Abstract : Black hole mergers are not fully understood - the details of the two apparent horizons becoming one is unclear due to the non-linear nature of the merger process. Recent numerical work has shown that there is an appearance of self-intersecting marginally outer-trapped surfaces (MOTS) during the black hole merger [1903.05626]. Following papers have found similarly behaving MOTS in a Schwarzschild black hole, where a seemingly infinite number of self-intersecting MOTS were found [2005.05350]. This talk introduces new phenomena that occur in the presence of an inner horizon. For Reissner-Nordstrom and Gauss-Bonnet black holes, we find that the maximum number of self-intersections becomes finite with the MOTS parameter space deeply dependent on the interior structure of the black hole and in particular the stability of the inner horizon [2111.09373].