This article presents a multi-mode explicit controller for constrained linear systems with bounded disturbances using a switching strategy based on Model Predictive Control (MPC). In the proposed approach, the system switches among several MPC controllers having different performance levels. The switching is done so as to achieve increasing levels of performance as time evolves, reaching the desired controller in finite time steps. The conditions needed for switching and robust convergence of the multi-mode MPC controllers are provided. Compared with standard robust explicit MPC implementations, the proposed approach has the flexibility of having a large domain of attraction, a good asymptotic behaviour and a small number of partitions.