The effect of addition of A homopolymer chains to HEX phases formed by cylindrical micelles obtained by dissolving an AB diblock copolymers in an A selective solvent was investigated. The following general trends were observed: (i) order-order transitions from HEX -> Gyroid (G), Lamellae (LAM); (ii) the inter-cylinder spacing of the HEX phase increased; (iii) when the homopolymer molecular weight and concentration was high, macrophase separation of the system occurred. The A homopolymer chains do not mix significantly with the A domain of the diblock due to excluded volume interactions, causing the Corona chain brush to contract. As a result, order-order transitions that reduce the interfacial curvature are observed.