  We study the possibility of realizing quantum anomalous Hall effect (QAHE)
with tunable Chern number through doping magnetic elements in the multi-layer
topological insulator film. We find that high Chern number QAHE phases exist in
the ideal neutral samples and it can make transition to another QAHE phase
directly by means of tuning the exchange field strength or sample thickness.
With the help of an extended Haldane model, we demonstrate the physical
mechanism of the tunable Chern number QAHE phase. Further, we study the
phenomena in the realistic samples with the Fermi energy being
gating-modulated, where the multiple-integer QAHE plateaus remain and two
separated QAHE phase are connected by metallic phase. The stability of the high
Chern number QAHE phase is also discussed.
