We examine the question of coexistence of three microbial populations competing for two complementary rate-limiting substrates in configurations of interconnected chemostats. It is known that coexistence of two populations competing for two rate-limiting substrates is possible in a single chemostat, but coexistence is not possible when three populations are involved. We examine whether coexistence of three populations becomes possible by considering configurations of two or three interconnected chemostats, thus allowing for effects of spatial heterogeneity. Computational analysis of the model equations indicates that in the case of two chemostats coexistence is possible only for specific discrete parameter values where the system is structurally unstable and therefore the coexistence state is not practically attainable, whereas in the case of three chemostats coexistence is possible for a whole range of parameter values where the system is structurally stable and therefore the coexistence state can be realized in practice.