  Thin films provide a versatile platform to tune electron correlations and
explore new physics in strongly correlated materials. Epitaxially grown thin
films of the alkali-doped fulleride K$_{3+x}$C$_{60}$, for example, exhibit
%various intriguing phenomena, including Mott transitions and
superconductivity, depending on dimensionality and doping. Surprisingly, in the
trilayer case, a strong electron-hole doping asymmetry has been observed in the
superconducting phase, which is absent in the three-dimensional bulk limit.
Using density-functional theory plus dynamical mean-field theory, we show that
this doping asymmetry results from a substantial charge reshuffling from the
top layer to the middle layer. While the nominal filling per fullerene is close
to $n=3$, the top layer rapidly switches to an $n=2$ insulating state upon hole
doping, which \textcolor{black}{implies a} doping asymmetry of the
superconducting gap. The interlayer charge transfer and layer-selective
metal-insulator transition result from the interplay between crystal field
splittings, strong Coulomb interactions, and an effectively negative Hund
coupling. This peculiar charge reshuffling is absent in the monolayer system,
which is an $n=3$ Mott insulator, as expected from the nominal filling.
