This paper investigates the region stability for switched linear systems whose subsystems have different equilibria, which are referred to multi-equilibrium switched linear systems, and proposes a number of new results on the region stability analysis. Through investigating the dynamical behavior of the multi-equilibrium switched system, a Common Lyapunov-like (CL-like) function method is ... [Show full abstract] established for the region stability, based on which several new approaches to the region stability analysis are then obtained. It is shown that the main results obtained in this paper not only guarantee the region stability of the multi-equilibrium switched linear system under arbitrary switching, but also provide several new methods to determine the corresponding stable regions. Finally, several illustrative examples with numerical simulations are studied by using the results obtained in this paper. Study of examples shows that our analysis methods work very well in analyzing the region stability of some classes of multi-equilibrium switched linear systems.