As far as solid, liquid, gas, plasma go, why is plasma the highest state?
Are there any other states of matter?
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If by highest, you mean temperature (proportional to mean kinetic energy of the particles), then the plasma state is "higher" than the other states you list.
I think that there are other "higher" states of matter. For example, when it becomes energetically favorable for protons and electrons to combine into neutrons, you get a state called "neutron degenerate matter". (By the way, have you ever read "Dragon's Egg"?)
An even "higher" state would be QCD matter, e.g., quark-gluon plasma.
Why is plasma the highest state.
The highest state in terms of what?
There are lots and lots of states of matter. Personally, I like Bose-Einstein Condensates, but just because it's so fun to say.
Not all materials fit into the 3 classic states. Plasma is only one of many. Glass, for example, isn't really a solid, but it's not a liquid either.
Wikipedia has a nice description of the states of matter
Well...Critical phases are characterized by the temperature where more fundamental degrees of freedom do appear. If you heat a solid, you can "melt" it to reveal its molecules, revealing firstly "liquid" and later gases...Where molecules (or atoms!) move freely. Plasmas as merely a phase where matter is so hot that electrons go free like a vegetables inside a soup, so they reveal the electrons in the atoms (fundamental or elementary so far). What is next? The next higher TEMPERATURE state is not the melting of electrons (we do know if electrons are elementary or not), but protons or more generally hadrons. Hadrons deconfine at higher temperature than atoms, indeed you will need about 10¹²K degrees to make quark-gluon plasma an reveal (melting hadrons) the inner substructure of hadrons. Well, ... The next issue would be...Something else? Yes. At least from theoretical reasons we do know additionally 2 temperatures where something "higher" happen at very very high temperature...What is it? They are two temperatures where a phase transition of higher type, as you called it, will happen:
Final note: if electrons or quarks were indeed bound states by some hyperforce, of preonic particles, well, they should have also a higher transition temperature.