We investigate high-Chern-number quantum anomalous Hall (QAH) phases in sliding bilayer hexagonal lattices. Lateral displacement between layers acts as a symmetry-reduction mechanism that breaks $C_3$ rotational symmetry and shifts band crossings to generic momenta in the Brillouin zone. When time-reversal symmetry is broken by Haldane-type complex next-nearest-neighbor hoppings, these crossings are gapped, yielding insulating phases with Chern numbers up to $\left|C\right|=4$. The large topological charge arises from asymmetric interlayer hybridization mediated by skew hopping channels, which enable multiple inequivalent band inversions within the four-band manifold and redistribute the Berry curvature. Ribbon calculations confirm the corresponding number of chiral edge modes. Our results establish sliding-controlled interlayer hybridization as a symmetry-driven route to nonadditive high-Chern QAH phases in bilayer systems.

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• Edge states
• Bilayer films
• Topological materials
• Tight-binding model