non-linear devices are power dependent, that means on 1V, it has a circuit model, on 10V, it is going to have a completely different circuit model. Usually, people use small signals on biased non-linear devices so that it can behave approximately linear, but this is not the ideal solution. It is very inconvenient to extract equivalent circuit at every input power and it is not quite accurate.
Back to your question, there should have no S-parameter defined over non-linear networks, S-parameter assumes pure passive linear network. You will have >0 components and out-of-input-freq-range components if you calculate your S-parameter in the traditional way.