  The recent discovery of the unprecedentedly superluminous transient
ASASSN-15lh (or SN 2015L) with its UV-bright secondary peak challenges all the
power-input models that have been proposed for superluminous supernovae. Here
we examine some of the few viable interpretations of ASASSN-15lh in the context
of a stellar explosion, involving combinations of one or more power inputs. We
model the lightcurve of ASASSN-15lh with a hybrid model that includes
contributions from magnetar spin-down energy and hydrogen-poor circumstellar
interaction. We also investigate models of pure circumstellar interaction with
a massive hydrogen-deficient shell and discuss the lack of interaction features
in the observed spectra. We find that, as a supernova ASASSN-15lh can be best
modeled by the energetic core-collapse of a ~40 Msun star interacting with a
hydrogen-poor shell of ~20 Msun. The circumstellar shell and progenitor mass
are consistent with a rapidly rotating pulsational pair-instability supernova
progenitor as required for strong interaction following the final supernova
explosion. Additional energy injection by a magnetar with initial period of 1-2
ms and magnetic field of 0.1-1 x 10^14 G may supply the excess luminosity
required to overcome the deficit in single-component models, but this requires
more fine-tuning and extreme parameters for the magnetar, as well as the
assumption of efficient conversion of magnetar energy into radiation. We thus
favor a single-input model where the reverse shock formed in a strong SN
ejecta-CSM interaction following a very powerful core-collapse SN explosion can
supply the luminosity needed to reproduce the late-time UV-bright plateau.
