The behaviour of a multi-degree-of-freedom vibro-impact system is studied using a 2 degree-of-freedom impact oscillator as a motivating example. A multi-modal model is used to simulate the behaviour of the system, and examine the complex dynamics which occurs when both degrees of freedom are subjected to a motion limiting constraint. In particular, the chattering and sticking behaviour which occurs for low forcing frequencies is discussed. In this region, a variety of non-smooth events can occur, including newly studied phenomena such as sliding bifurcations. In this paper, the multiple non-smooth events which can occur in the 2 degree-of-freedom system are categorised, and demonstrated using numerical simulations.