Concept lattices are well-known conceptual structures that organise interesting patterns—the concepts—extracted from data. In some applications, such as software engineering or data mining, the size of the lattice can be a problem, as it is often too large to be efficiently computed, and too complex to be browsed. For this reason, the Galois Sub-Hierarchy, a restriction of the concept lattice to introducer concepts, has been introduced as a smaller alternative. In this paper, we generalise the Galois Sub-Hierarchy to n-lattices, conceptual structures obtained from multidimensional data in the same way that concept lattices are obtained from binary relations.