Let M be a manifold. A PDE system R ⊆ J 1 m M can be prolonged to another one R * ⊆ T * M [10]). In analogy with the higher-order symmetries, symmetries of R * will be called higher-dimensional symmetries of R. For a broad class of PDE systems we prove that every (infinitesimal or finite) symmetry of R comes from another one of R * . We show that R * does not have internal (infinitesimal) symmetries (modulo trivial symmetries). This fact allows us, in the infinitesimal case, to compute the internal symmetries of R as external symmetries of R * . We also give an algorithmic method to obtain solutions of R invariant by a given internal symmetry.Let M be a smooth manifold with dim M = n and J k m M the space of k-jets of m-dimensional submanifolds of M. Let R ⊆ J k m M be a PDE system. Classically, a symmetry of R is a diffeomorphism of M whose prolongation to J k m M leaves R invariant or, infinitesimally, a vector field in M whose (m, k)-prolongation is tangent to R. These symmetries are called point symmetries because they come from transformations of the manifold M. However, more general symmetries can be considered: Lie himself dealt with symmetries not as point transformations, but as contact transformations; that is, diffeomorphisms of J k m M that preserve the contact system. In light of Bäcklund's theorem, we obtain new transformations only in the case m = n − 1. In any case, we continue regarding the system R from outside, considering geometrical transformations of the ambient J k m M that leave R invariant. These symmetries are called external symmetries. However, it seems more reasonable to consider transformations of R itself that preserve the contact system restricted to R. Such transformations are called internal symmetries of R. It is obvious that, by restriction, each external symmetry of R gives an internal one, and, in many cases, these are the only internal symmetries (see [6], [7, pp. 116-121]).Another important class of symmetries that generalize contact transformations is the class of higher-order symmetries. A PDE system can be considered not only as itself but together with its prolongations to all orders. The transformations that preserve the contact system in the infinite jet space and leave the infinite prolongation of the system invariant are called higher-order symmetries. Unlike the classical theory, there are no internal higher-order symmetries (see [7, p. 162]). The relationship between higher-order symmetries and internal symmetries is investigated in depth, in the infinitesimal case, in [6]. There the authors prove for a broad class of equations that every internal symmetry arises from a first-order generalized symmetry.This paper deals with a new class of symmetries and its connection with other kinds of symmetries. Let R ⊆ J 1 m M be a PDE system. Following [9,10] we can consider the 'prolongation' of R to J 1 r M (r > m) (prolongation with respect to