Of course you can have multiple parties.
The current system in the US, of course, is set up against it.
In some places, you see a parliamentary system where the heads of state must be elected by a majority. Often you'll see a bunch of small parties banding together to form coalitions. Of course, the result is often something like Italy, where you have governments failing with some regularity due to shifting coalitions and demands.
In others, like France, you have a "runoff" system where, if no candidate has a majority, the top two vote-getters proceed to a second election. This leads to situations like France, where fragmentation among the many small leftist parties created a recent election featured a run-off between the mainstream right Chirac (yes, he's a conservative) and the neofascist Le Pen.
Of course, the US system, with a "winner take all" approach to electoral votes at the state level, and those electoral votes being assigned on some bizarre method of 2+the number of congressmen in the state, is pretty darn irrational too.
As Perot and Nader have shown, third parties often play the role of "spoiler", pushing the outcome of the presidential elections in the direction opposite to the general sentiment of the people.
You'd hope things were easier at the local, congressional and senatorial level, and to a certain degree they are, but remember that here is one area Democrats and Republicans can agree on: they don't want a third party mucking things up. At least they agreed until Bush had to be reelected (This is why the GOP support for Nader may make good short-term sense, but in the long term, it's a bad idea).
So they make rules to exclude third parties. Heck, you can even earmark part of your income taxes to go to the GOP or DNC if you so choose.
That's also why these 527s (or whatever their number is) are so impressive: while their use in this election is rather limited, in theory they can control large sums of election money tied to issues instead of candidates. Not that it's happened yet.
