  There are notable similarities between the marginally outer trapped surfaces
(MOTSs) present in the interior of a binary black hole merger and those present
in the interior of the Schwarzschild black hole. Here we study the existence
and properties of MOTSs with self-intersections in the interior of more general
static and spherically symmetric black holes and coordinate systems. Our
analysis is carried out in a parametrized family of
Painlev{\'e}-Gullstrand-like coordinates that we introduce. First, for the
Schwarzschild spacetime, we study the existence of these surfaces for various
slicings of the spacetime finding them to be generic within the family of
coordinate systems we investigate. Then, we study how an inner horizon affects
the existence and properties of these surfaces by exploring examples: the
Reissner-Nordstr\"om black hole and the four-dimensional Gauss-Bonnet black
hole. We find that an inner horizon results in a finite number of
self-intersecting MOTSs, but their properties depend sensitively on the
interior structure of the black hole. By analyzing the spectrum of the
stability operator, we show that our results for two-horizon black holes
provide exact-solution examples of recently observed properties of unstable
MOTSs present in the interior of a binary black hole merger, such as the
sequence of bifurcations/annihilations that lead to the disappearance of
apparent horizons.
