We analyze when symbolic dynamical systems have intermediate relative entropies for two symbolic spaces (X, o1) and (Y, o2). By this is understood to study the denseness of relative measure-theoretic entropies in the interval [0, h(v, o1)], where h(v, o1) is a relative topological entropy of the shift o1 with respect to a o2-invariant measure  in Y . We prove that for irreducible shifts with the (strong) specification property as introduced by Bowen, the set of the relative measure-theoretic entropies is dense in the above mentioned sense. To this, we use the decomposition of factor codes of Yoo and a variational principle for relative entropies given by Barral and Feng.