Multimode nonlinear optics is used to overcome a long-standing limitation of fiber optics, tightly phase locking several spatial modes and enabling the coherent transport of a wave packet through a multimode fiber. A similar problem is encountered in the temporal compression of multimillijoule pulses to few-cycle duration in hollow gas-filled fibers. Scaling the fiber length to up to 6 m, hollow fibers have recently reached 1 TW of peak power. Despite the remarkable utility of the hollow fiber compressor and its widespread application, however, no analytical model exists to enable insight into the scaling behavior of maximum compressibility and peak power. Here we extend a recently introduced formalism for describing mode locking to the analog scenario of locking spatial fiber modes together. Our formalism unveils the coexistence of two soliton branches for anomalous modal dispersion and indicates the formation of stable spatiotemporal light bullets that would be unstable in free space, similar to the temporal cage solitons in mode-locking theory. Our model enables deeper understanding of the physical processes behind the formation of such light bullets and predicts the existence of multimode solitons in a much wider range of fiber types than previously considered possible.