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This work addresses whether a reaction network, taken with mass-actionkinetics, is multistationary, that is, admits more than one positive steadystate in some stoichiometric compatibility class. We build on previous work onthe effect that removing or adding intermediates has on multistationarity, andalso on methods to detect multistationarity for networks with a binomial steadystate ideal. In particular, we provide a new determinant criterion to decidewhether a network is multistationary, which applies when the network obtainedby removing intermediates has a binomial steady state ideal. We apply thismethod to easily characterize which subsets of complexes are responsible formultistationarity; this is what we call the \emph{multistationarity structure}of the network. We use our approach to compute the multistationarity structureof the $n$-site sequential distributive phosphorylation cycle for arbitrary n.

The multistationarity structure of networks with intermediates and a binomial core network