The infinite-bin model, introduced by Foss and Konstantopoulos in [3], describes the Markovian evolution of configurations of balls placed inside bins, obeying certain transition rules. We prove that we can couple the behaviour of any finite number of balls, provided at least two different transition rules are allowed. This coupling makes it possible to define the regeneration events needed by Foss and Zachary in [4] to prove convergence results for the distribution of the balls.