The transitions between epithelial (E) and mesenchymal (M) cell phenotypes are essential in many biological processes like tissue development and cancer metastasis. Previous studies, both modeling and experimental, suggested that in addition to E and M states, the network responsible for these phenotypes exhibits intermediate phenotypes between E and M states. The number and importance of such states is subject to intense discussion in the EMT community. Results: Previous modeling efforts used

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... raditional bifurcation analysis to explore the number of the steady states that correspond to E, M and intermediate states by varying one or two parameters at a time. Since the system has dozens of parameters that are largely unknown, it remains a challenging problem to fully describe the potential set of states and their relationship across all parameters. We use the computational tool DSGRN (Dynamic Signatures Generated by Regulatory Networks) to explore the intermediate states of an EMT model network by computing summaries of the dynamics across all of parameter space. We find that the only attractors in the system are equilibria, that E and M states dominate across parameter space, but that bistability and multistability are common. Even at extreme levels of some of the known inducers of the transition, there is a certain proportion of the parameter space at which an E or an M state co-exists with other stable steady states. Conclusions: Our results suggests that the multistability is broadly present in EMT network across parameters and thus response of cells to signals may strongly depend on their history and genetic background.