We investigate new paths to supermassive black hole formation by considering the general relativistic evolution of a differentially rotating polytrope with a toroidal shape. We find that this polytrope is unstable to nonaxisymmetric modes, which leads to a fragmentation into self-gravitating, collapsing components. In the case of one such fragment, we apply a simplified adaptive mesh refinement technique to follow the evolution to the formation of an apparent horizon centered on the fragment. This is the first study of the onset of nonaxisymmetric dynamical instabilities of supermassive stars in full general relativity.