Distributed software systems that determine virtual communication structures on top of physical networks, the overlay networks, are a well-established approach to build various applications of collective adaptive systems such as peer-to-peer file sharing, multimedia multi-casting, aggregation in distributed databases or routing in wireless sensor networks. Despite the significance of this approach to apply collective adaptive systems in practice, applications based on overlay networks often result in a complex integration of the operational logic with topological management. This approach results in low abstraction, modularity and reconfigurability of applications that require one or more overlay networks to operate. This paper challenges this design approach by introducing the notion of overlay services that provide generic application capabilities of a broad application scope enabled by one or more overlay networks. This paper contributes the multi-level conceptual architecture of ASMA that structures and guides the realisation of overlay services by using only a few lines of high-level algorithmic expressions. Two overlay services realised according to ASMA provide a proof-of-concept for the high abstraction, modularity and reconfigurability achieved in collective adaptive systems based on overlay networks.