Abstract The outcome of a major evolutionary transition is the aggregation of independent entities into a new synergetic level of organisation. Classical models involve either pairwise interactions between individuals or a linear superposition of these interactions. However, major evolutionary transitions display synergetic effects: their outcome is not just the sum of its parts. Multiplayer games can display such synergies, as their payoff can be different from the sum of any collection of two-player interactions. Assuming that all interactions start from pairs, how can synergetic multiplayer games emerge from simpler pairwise interaction? Here, we present a mathematical model that captures the transition from pairwise interactions to synergetic multiplayer ones. We assume that different social groups have different breaking rates. We show that non-uniform breaking rates do foster the emergence of synergy, even though individuals always interact in pairs. Our work sheds new light on the mechanisms underlying a major evolutionary transition.