Overlay networks have emerged as a powerful paradigm to realise a large range of distributed services. However, as the number of overlays grows and the systems that use them become more interconnected, overlays must increasingly co-exist within the same infrastructure. When this happens, overlays have to compete for limited resources, which causes negative interferences. This paper takes an opposite view, and argues that coexisting overlays may also introduce positive synergies that can be exploited to benefit a distributed system. Unfortunately, and in spite of some pioneering work, this phenomenon is still poorly understood and has yet to be investigated systematically. To address this problem, this paper proposes a principled classification of synergies, and illustrates how it can be used to exploit synergies in a typical overlay platform targeting gossip protocols (GossipKit). We review in detail the risks and benefits of each identified synergy; we present experimental data that validate their added value, and finally discuss the lessons we have learnt from our implementation.