The STAR model is widely used to represent the dynamics of a certain variable recorded at several locations at the same time. Its advantages are often discussed in terms of parsimony with respect to space-time VAR structures because it considers a single coefficient for each time and spatial lag. This hypothesis can be very strong; we add a certain degree of flexibility to the STAR model, providing the possibility for coefficients to vary in groups of locations. The new class of models is compared to the classical STAR and the space-time VAR by simulations and an application.