Floquet engineering serves as a forceful technique for uncovering high Chern numbers of quantum anomalous Hall (QAH) states with feasible tunability in high-order topologically insulating plumbene, which is readily accessible for experimental investigations. Under the irradiation of right-handed circularly polarized light, we predict a three-stage topological phase transition in plumbene, whether it is in a free-standing form or grown on h-BN. Initially, a metallic state evolves into a $K(K^{\prime }$)-valley-based QAH state with a Chern number of −8, which then decreases to −6 after the valley gap closes. Finally, a band inversion occurs at the $\mathrm{\Gamma }$ point, resulting in a multichannel QAH state with $C=–3$. The trigonal warping model accounts for both $K(K^{\prime }$)-valley-based and $\mathrm{\Gamma }$-point-based QAH states. Additionally, growing plumbene on a non–van der Waals substrate eliminates the $K(K^{\prime }$)-valley-based topology, leaving only the $\mathrm{\Gamma }$-point-based QAH state with $C=+3$. Our findings propose the tunability of various high Chern numbers derived from high-order topological insulators, aiming to advance the next-generation dissipationless electronic devices.

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• Chern insulators
• Photoinduced effect
• Topological insulators
• Topological phase transition