Is quantum computing limited to a superposition of only two
In theory, it is not. Keep in mind that a qubit is a quantum analogue of the classical "bit" which has only two states $0$ and $1$. In principle, there is no limit to the dimension of the state space of a quantum system. There could even be an "infinite" dimensional separable Hilbert space (in short, separable means denumerable/countable with a one-one onto mapping to the natural numbers). For non-separable Hilbert spaces there are some complications involved.
In the context of quantum information systems with a state-space dimension greater than $2$ are called "qudits".
And yes, there has been ongoing work to make physical implementations of higher dimensional quantum systems, like qutrits (with trapped ions), as mentioned by @Andrew O, on their currently deleted answer (only users having the privilege to view deleted posts can see it at present).
Relevant paper: Qutrit quantum computer with trapped ions - A. B. Klimov, R. Guzmán, J. C. Retamal, and C. Saavedra
- @glS mentions here that in some cases making higher-dimensional quantum systems can, in fact, be easier, which is an interesting fact I did not know earlier.
In the context of photonics, for example, it is relatively easy to
generate states in high-dimensional Hilbert spaces, for example
exploiting the orbital angular momentum of single photons. See for
example 1607.05114 and the many
references therein, or Fickler
2012, in which they experimentally
demonstrate entanglement of states living in 600-dimensional Hilbert
It is also to be noted that the matter of non-separability is
absolutely a non-issue for practical implementation of whatever
protocol, and also that continuous variable quantum computation is a
big subject in quantum computing