This work addresses whether a reaction network, taken with mass-action kinetics, is multistationary, that is, admits more than one positive steady state in some stoichiometric compatibility class. We build on previous work on the effect that removing or adding intermediates has on multistationarity, and also on methods to detect multistationarity for networks with a binomial steady-state ideal. In particular, we provide a new determinant criterion to decide whether a network is multistationary, which applies when the network obtained by removing intermediates has a binomial steady-state ideal. We apply this method to easily characterize which subsets of complexes are responsible for multistationarity; this is what we call the multistationarity structure of the network. We use our approach to compute the multistationarity structure of the n-site sequential distributive phosphorylation cycle for arbitrary n.