Consider an iterated map that exhibits a period-doubling cascade. If two such maps are coupled, then the synchronised state will exhibit the same period-doubling cascade but there is also the additional possibility of symmetry-breaking bifurcations to non-synchronised states. By introducing a second parameter, a symmetry-breaking/period-doubling mode interaction can be induced. As the second parameter is varied, a secondary symmetry-breaking bifurcation may occur from the period 2 solutions, which will then be involved in another mode interaction at the next period-doubling bifurcation point. In this way, a cascade of mode interactions can occur. Both a local analysis of such a mode interaction and the global consequences together with a classification of different cases have been considered. Renormalisation theory has been used to determine the universal behaviour and parameter scalings of such a system.