  Quantum anomalous Hall (QAH) insulators host topologically protected
dissipationless chiral edge states, the number of which is determined by its
Chern number. Up to now, the QAH state has been realized in a few magnetic
topological insulators, but usually with a low Chern number. Here, we develop a
Dirac-fermion approach which is valuable to understand and design high Chern
numbers in various multilayers of layered magnetic topological insulators.
Based on the Dirac-fermion approach, we demonstrate how to understand and tune
high Chern numbers in ferromagentic MnBi$_{2}$Te$_{4}$ films through the van
der Waals (vdW) gap modulation. Further, we also employ the Dirac-fermion
approach to understand the experimentally observed high Chern numbers and
topological phase transition from the Chern number $C=2$ to $C=1$ in the
[3QL-(Bi,Sb)$_{1.76}$Cr$_{0.24}$Te$_{3}$]/[4QL-(Bi,Sb)$_{2}$Te$_{3}$]
multilayers. Our work provides a powerful tool to design the QAH states with a
high Chern number in layered magnetic topological insulator multilayers.
