The dependence of the optical communication interconnects on the electronics technology is a limitation for ultra-high-speed communications. Nanophotonics promises intriguing technologies to exceed these limitations. In this context, a silicon-based composite nanostructure is proposed to boost the magnetic Purcell enhancement one order of magnitude higher than a single hollow-disk resonator. The boosting effect relies on the near-field interaction between a hollow disk resonator and two larger rings. The engineering of the device is presented via simulations with the aim of obtaining the highest Purcell enhancement. Additionally, to reveal the underlying mechanism, the contribution of each multipole mode to the scattered intensity and near-field enhancement properties are analysed. Finally, the dependence of the Purcell factor on the position of the source is investigated. The results of this study may have a great potential to realize nanoscale light sources to be used in all-photonic chips for ultra-high-speed optical networks.