  Composite systems, where couplings are of two types, a combination of strong
dilute and weak dense couplings of Ising spins, are examined through the
replica method. The dilute and dense parts are considered to have independent
canonical disordered or uniform bond distributions; mixing the models by
variation of a parameter $\gamma$ alongside inverse temperature $\beta$ we
analyse the respective thermodynamic solutions. We describe the variation in
high temperature transitions as mixing occurs; in the vicinity of these
transitions we exactly analyse the competing effects of the dense and sparse
models. By using the replica symmetric ansatz and population dynamics we
described the low temperature behaviour of mixed systems.
