Yes, but among other things you'd need legislation requiring the existing parties to remove their chokehold on the political process. For instance, when you register to vote for the first time in the United States, you have to register as a Republican, a Democrat, or (in most instances) "other" or "independent". Non-Republican-or-Democrats are at a disadvantage out of the gate. From the get-go, the only hope for most serious candidates is to identify as either a Republican or a Democrat. Run as an independent, no matter how great your platform, and you get limited financial assistance compared to your major-party opponents. Successful 3rd-party candidates are either rich and famous (Jesse Ventura) or extremely rich (Ross Perot). (I know Perot didn't win anything, but getting 19% of the vote in a presidential election is pretty impressive.) In the words of P.J. O'Rourke, "In Mexico, one party has stolen every election since 1929. As distinguished from America, where 2 parties have stolen every election since 1848."

Could such legislation as listed above ever be enacted? Pretty unlikely, seeing who writes the laws.

The 2-party system is the byproduct of a republican form of government. It has nothing to do with the United States using plurality voting rather than some more complex method.

Ask any political science graduate: compared to other nations', parties in the U.S. are weak. Anyone seeking office is free to run as a member of the party of his choice. (See lifelong Democrat Michael Bloomberg strategically running as a Republican, etc.) Then, win your intra-party primary and congratulations, you're on the general election ballot. Republican and Democratic officeholders in the U.S. are not beholden to the "party line", and not punished - at least not explicitly - if they vote against the wishes of party leadership. That's the exact opposite of how it works in parliamentary democracies. In Canada, for instance, pretty much every Liberal votes the same way on every issue. Same deal for the Conservatives, and the New Democrats. Don't, and you might never get to run for election again.

So regardless of how many factions the United States started with, it had to get down to two at some point. If you started from scratch with 3 parties of equal strength, and no one holding a majority, sooner or later the two more closely aligned parties are going to realize that they're stronger together than apart.