In this paper, we present the concept of a multi-connected handle operation to create complex high genus virtual sculptures. We have developed and implemented a simple procedure to create handles that connect a set of user-selected faces in 3D. To create multi-connected handles, we first create a convex connector mesh. We then connect each selected face to this connector surface with a simple one segment handle. If the connector mesh is completely exterior to the original mesh, we get a multi-connected handle. If it lies inside of the original mesh we get a multi-connected hole.