The competition between wind and buoyancy forces acting on a naturally ventilated building with one upwind and one downwind opening and a distributed heat source can lead to multiple steady states. This study considers the impact of a second downwind opening on the existence of these multiple steady states. It is found that if this new opening exceeds a critical area, then the multiple steady states are eliminated, and the transition from buoyancy to wind dominated flow is continuous. This critical area is shown to be a function of the relative heights of the three windows. The predictions of the model are in accord with new laboratory experiments, and the implications for building design are discussed.