What other possible quantum systems are there besides two-level/two-state quantum systems? Sorry for the rather odd question, but here it is:
There are a ton of references and research literature on two-state quantum systems, and their derived properties and mathematics. I'm familiar with the properties of two-level/two-state quantum systems.
However, are there other types of quantum systems other than two-level/two-state quantum systems, and if so, what are some examples? Are there any canonical references on the subject of these systems?
Help a brother out :)
 A: Two state quantum systems show up often in the literature for a few reasons:

*

*These are the simplest/most basic quantum systems, and are thus easy to understand and study.

*More complex systems can be made by putting together multiple two states systems. For instance if you put two, two-state systems together, you now have a 4 state system, and if you put $n$ two-state systems together, you have a $2^n$ state system.

*Classically, all logical computations can be represented by a list of two-state options (e.g. true/false or 0/1) plus operations on that list (which in general depends on the value of the list itself). This is the basis of all modern computer systems and due to the growth of quantum computing, there is a heavy emphasis on the quantum version of this (systems composed of multiple two-state systems we call quantum bits or qubits)

Now your question is asking what states exist other than a single isolated two-state quantum system and the answer is, literally everything else. This includes systems that can be broken into smaller components, including systems made of many interacting two-state quantum systems (as mentioned previously). So any quantum computer that has more than a single qubit can be thought of as an example of such a system.
There are also things that can't be broken down into small sub-systems with a small discrete number of states (such as a two-state qubit). For instance the dynamics of fundamental particles (such as the position or momentum of a single electron) are described by continuous variables, and so these are examples of infinite-state systems.
Another type of system that shows up a lot as a basic quantum system (similar to two-state systems) is the quantum harmonic oscillator. This model is often useful as it is both analytically solvible, and represents many phenomena related to continuous systems in/around some equilibrium state (for instance the center of mass of a single ion in an ion trap or the amount of current flow in a superconducting circuit resonator).
An even more complicated type of quantum system are quantum fields. For instance an electromagnetic field can take on any strength at some point in space and so is similar to the infinite-dimensional continuous variable systems mentioned above. Interestingly enough, the strength of any specific electromagnetic field mode can also be described by certain discrete levels as well (similar to the discrete levels in a quantum harmonic oscillator). These levels are equivalent to the photon description of light, e.g. the zero-th, first, and second levels represent there being zero, one, or two photons in that specific electromagnetic field mode, and in general the $n$th mode represents a state of $n$ photons.
