In this work, the problem of master–slave outer synchronization in different inner–outer network topologies is presented. Specifically, the studied inner–outer network topologies are coupled in master–slave configuration, where some particular scenarios concerning inner–outer topologies are addressed in order to disclose a suitable coupling strength to achieve outer synchronization. The novel MACM chaotic system is used as a node in the coupled networks, which presents robustness in its bifurcation parameters. Extensive numerical simulations are presented where the stability of the inner–outer network topologies is analyzed through a master stability function approach.