In previous work, we proposed an algebra whose operators allow to specify the valid compound terms of a faceted taxonomy, in a flexible manner (by combining positive and negative statements). In this paper, we treat the same problem but in a more general setting, where the facet taxonomies are not independent but are (possibly) interrelated through narrower/broader relationships between their terms. The proposed algebra, called Interrelated Facet Composition Algebra (IFCA), is more powerful, as the valid compound terms of a faceted taxonomy can be derived through a smaller set of declared valid and/or invalid compound terms. An optimized (w.r.t. the naive approach) algorithm that checks compound term validity, according to a well-formed IFCA expression, and its worst-time complexity are provided.