Although virtual reality hardware is now widely available, the uptake of real walking is hindered by the fact that it requires often impractically large amounts of physical space. To address this, we present VirtualSpace, a novel system that allows overloading multiple users immersed in different VR experiences into the same physical space. VirtualSpace accomplishes this by containing each user in a subset of the physical space at all times, which we call tiles; app-invoked maneuvers then shuffle tiles and users across the entire physical space. This allows apps to move their users to where their narrative requires them to be while hiding from users that they are confined to a tile. We show how this enables VirtualSpace to pack four users into 16m2. In our study we found that VirtualSpace allowed participants to use more space and to feel less confined than in a control condition with static, pre-allocated space.