We do have more than two choices on the typical ballot. Mine, for example, usually has a demwit, a retardican, a librarian, a greenie, a suckialist, and often one or two more.
In practical terms, however, we do have a two party system, and so it has been since Jefferson invented it. The majors have so deeply entrenched themselves with entry, campaign and financial barriers that none of the rest can compete but in limited localities. There is no legal mandate for only two parties, and so there is no law than can be repealed to allow more into the house, but unless a third one can gain enough representatives at all levels of government to do away with those filters that have been legislated the system is not going to change.
As for doing away with parties, there is a law that applies. It's the Bill of Rights' freedom of assembly, which forbids the federal government from interfering. They're here to stay.