We investigate the possibility of “going beyond” Turing in the terms of Automaton-like P Colonies (APCol systems, for short), variants of P colonies processing strings as their environments. We use the notion of teams of agents as a restriction for the maximal parallelism of the computation. In addition, we assign a colour to each team. In the course of the computation, the colour is changing according to the team that is currently active. We show that we can simulate red-green counter machines with APCol systems with two-coloured teams of minimal size. Red-green counter machines are computing devices with infinite run on finite input that exceed the power of Turing machines.