Competition between two-sided platforms is shaped by the possibility of multihoming. If users on both sides singlehome, each platform provides users on either side exclusive access to its users on the other side. In contrast, if users on one side can multihome, platforms exert monopoly power on that side and compete on the singlehoming side. This paper explores the allocative effects of such a change from single- to multihoming. Our results challenge the conventional wisdom, according to which the possibility of multihoming hurts the side that can multihome, while benefiting the other side. This is not always true: the opposite may happen or both sides may benefit.