Are there more than three states of matter?
Yes, over 10+ states of matter have been discovered, though plasma and BEC are considered to be the 2 other major states (in addition to the "Big 3").
Yes, there are many more states of matter that scientists have discovered, but only 3 are taught to middle school students. 2 of these are added to the "Big 3" states: plasma and Bose-Einstein condensate (BEC).
I won't go over the 3 main states as it is primary knowledge.
Plasma is probably the most common state in the universe - not Earth. Plasma is essentially ionized gas. This means that the particles are highly charged and has a lot of kinetic energy. Most of the celestial bodies in space are balls of plasma, and neon signs are also plasma.
You can get plasma by ionizing gas. That said, you can de-ionize plasma to get gas, "A plasma is an ionized gas, a gas into which sufficient energy is provided to free electrons from atoms or molecules and to allow both species, ions and electrons, to coexist" (education.jlab.org).
BEC is matter in which the particles have little to no kinetic energy. The energy is so minuscule it is considered non-existent. This results in the particles in the matter to not be individual, but acts as one single atom.
This is achieved when kinetic energy is removed - cooled down, "At this extremely low temperature, molecular motion comes very close to stopping altogether. Since there is almost no kinetic energy being transferred from one atom to another, the atoms begin to clump together" (LiveScience.com).
Here is a diagram of the 5 states of matter:
As you go right, you are adding kinetic energy (heat). Upon plasma, you ionize the particles. Going left is the opposite.
Hope this helps :)