In extreme working conditions such as poor road conditions, the low road adhesion coefficient is easy to cause the tire cornering characteristics curve to be in the nonlinear domain, making the vehicle system in the critical instability state. To this end, this paper proposes a cascade deep learning framework combining multi-model predictive control (MMPC) and LSTM tire cornering stiffness estimation (TCSE) neural network and designs a stability control strategy of vehicle four-wheel steering system considering tire nonlinear cornering characteristics. The four-wheel steering system and vehicle tire dynamic model are analyzed and established, and the online estimation method of tire cornering stiffness and MMPC's sub-model classification method is developed. On this basis, the tire angle is creatively introduced as the phase plane stability region boundary, used to design the MMPC controller's boundary condition. The hardware in the loop test results shows that compared with the existing research, the strategy proposed in this paper can effectively improve the tracking accuracy of the target steering signal and ensure the system's stability when the road adhesion coefficient is low.