Cophylogenetics is the study of the evolutionary relationships between taxonomical units that are believed to be evolving concomitantly. We examine the combinatorial properties of the cophylogenetic distance metric, k-interval cospeciation, which was introduced by Huggins, Owen and Yoshida in their 2012 paper, "First steps toward the geometry of cophylogeny." We determined that k-interval cospeciation is a unique discrete distance metric which can quantify a degree of global congruence between two phylogenetic trees while allowing for local incongruence. We counted the size of the neighborhood of trees which satisfy the largest possible k-interval cospeciation with a given tree. Due to the way this neighborhood of trees grows as a proportion of all possible trees, we believe that k-interval cospeciation may prove useful for analyzing data obtained through simulations.