Many mechanisms have been proposed for ethylene hydrogenation on catalytic surfaces. In a companion article we discussed how isothermal multiple steady-state data can be used to discriminate between rival candidate mechanisms. While most catalytic mechanisms have the capacity to support some pair of steady states, they will not usually have the capacity to support a particular pair of steady states observed in the laboratory. The companion article described how chemical reaction network theory can be used to determine whether multiple steady-state data are consistent with a given mechanism. Multiple steady-state data had been obtained previously for ethylene hydrogenation over a rhodium catalyst in an isothermal CFSTR. In this article, these data are used to discriminate between a total of 80 single- and multiple-pathway mechanisms. Given certain assumptions, it will be seen that only nine of the 80 mechanisms are consistent with the data. The purpose of this article is not to favor one mechanism over another, but to demonstrate the type of refined mechanism discrimination that is possible using even fragmentary multiple steady-state data.