Technically we can have any number of political parties and do. I believe I had candidates representing five parties running for my state’s auditor this last time.

However various conditions have always prevented other parties from building a competitive national presence. Things like name recognition and the vast amount of money spent in a typical election is very difficult for a new party. On the occasion when someone has reached the legislature, you can’t really do anything without a party behind you, so it’s tough to make an impact. People complain about the voting system, but it just means there’s no second place: each of the two will win different areas but very tough for a third party to break in since there’s no second place or third place.