As described in #905:

Any reason why initial_response, step_response, and forced_response can’t/shouldn’t be modified to be compatible with NonlinearIOSystems? It was a bit confusing to students in my class last quarter why they had to switch to a different simulation function if they included a nonlinear system in their InterconnectedSystem.

It should be possible to make all of the systems work for a NonlinearIOSystem.

For the impulse response, we could take the linearization of the system at the initial condition and then use that to reset the initial condition, though I'd want to think that through make sure that is the right thing to do mathematically.