After "Track Volume" (in example, so after you have selected parameter in question) insert Action "Value Current".
Now set the switch (in GUI) to the state you can't change to. Press your button. Open "Overview" Tab.
You should see "Current, timeout touch -> X.XX". The value is from 0. to 1.. That way you know which value you need.
Then calculate the number of states you need, with 3 it covers "0 - 0.33, 0.33 - 0.66, 0.66 - 1", with 4: "0. - 0.25, 0.25-0.5, 0.5 - 0.75, 0.75 - 1.".
I hope you have got the idea
These things are tricky, I know. But you want "trick" the DAW and plug-in, they have not foreseen such behavior and so there is no simple way.
BTW there is right way for plug-in and DAW to implement 3state switch parameters, describing what they are in VST API. But almost no-one is
doing that. BTW if you have 3 states and values are from 0.0 to 0.1, is that not "logical" to use 0, 0.5 and 1 for them? For some reason plug-in developers not always think logical...