We propose an algorithm to construct a set of interfaces that separate the connected components of a multi-valued volume dataset. While each single interface is a manifold triangle mesh, two or more interfaces may join consistently along their common boundaries, i.e. there are no T-junctions or gaps. In contrast to previous work, our algorithm classifies and removes the topological ambiguities from the volume before extracting the interfaces. This not only allows for a simple and stable extraction algorithm, but also makes it possible to include user constraints.