Coupling transition metal or lanthanide ions through a radical bridging ligand is a promising route to increase performances in the area of single molecular magnets. A better understanding of the underlying physical mechanisms governing the magnetic exchange couplings is thus of valuable importance to design future compounds. Here, couplings in three series of metal-radical-metal compounds based on transition metal ions are investigated by means of the decomposition/recomposition methods. This work presents the generalisation and first application of the method to systems with an arbitrary number of magnetic centres featuring several unpaired electrons. Thanks to the decomposition into the three main contributions (direct exchange, kinetic exchange, and spin polarisation) as well as a description in terms of electron-electron interactions, we study the influence of the nature of the metal centre and the radical ligand on the couplings. We combine the energetic contributions extracted with orbital and charge population analysis to rationalise the results.