Let H be a complex infinite-dimensional separable Hilbert space. If T is an isometry acting on H, then the von Neumann-Wold decomposition theorem asserts that T can be expressed as a direct sum of the unilateral shift (of some multiplicity) and a unitary operator. We establish a multivariate generalization of the von Neumann-Wold decomposition and explore some of the implications of that generalization. In particular we derive a universal representation theorem for members of a special class of spherical isometries and verify that any member of that class is hyperreflexive.