  Superexponential systems are characterized by a potential where dynamical
degrees of freedom appear in both the base and the exponent of a power law. We
explore the scattering dynamics of many-body systems governed by
superexponential potentials. Each potential term exhibits a characteristic
crossover via two saddle points from a region with a confining channel to two
regions of asymptotically free motion. With increasing scattering energy in the
channel we observe a transition from a direct backscattering behaviour to
multiple backscattering and recollision events in this channel. We analyze this
transition in detail by exploring both the properties of individual many-body
trajectories and of large statistical ensembles of trajectories. The
recollision trajectories occur for energies below and above the saddle points
and typically exhibit an intermittent oscillatory behaviour with strongly
varying amplitudes. In case of statistical ensembles the distribution of
reflection times into the channel changes with increasing energy from a
two-plateau structure to a single broad asymmetric peak structure. This can be
understood by analyzing the corresponding momentum-time maps which undergo a
transition from a two-valued curve to a broad distribution. We close by
providing an outlook onto future perspectives of these uncommon model systems.
