The qualitative capacity for multiple steady states in an isothermal homogeneous continuous flow stirred tank reactor is determined by the operative reaction network. Examples demonstrate that there is an extremely delicate relationship between reaction network structure and the possibility of multiple steady states. Nevertheless, by means of an easily constructed diagram, called the SCL graph, the capacity of complex reaction networks for multiple steady states can often be decided very quickly. Moreover, information carried by the SCL graph is sufficiently refined as to identify subtle distinctions between networks that can admit multiple steady states and very similar ones that cannot.