During recent decades, the equilibrium manifold expansion (EME) model has been considered as a powerful identification tool for complex industrial systems with the aim of system control and simulation. Based on a two-step “dynamic and static” identification method, an approximate nonlinear state-space model is built by using multiple polynomials. However, the existing identification method is only suitable for single-input (SI) systems, but not for multi-input (MI) systems, where EME models cannot guarantee global calculation stability. For solving such a problem, this paper proposes a corrected equilibrium manifold expansion (CEME) model based on gas turbine prior knowledge. The equilibrium manifold is extended in dimension by introducing similarity equations instead of the high dimensional polynomial fitting. The dynamic similarity criterion of similarity theory guarantees the global stability of the CEME model. Finally, the comparative test between the CEME model and the existing MI-EME model is carried out through case studies involving data that are generated by a general turbofan engine simulation. Simulations show superior precision and calculation stability of the proposed model in capturing nonlinear behaviors of the gas turbine engine.