Factions or parties are something humans do when there is an issue of mutual interest that motivates them. There is NO escaping it! In fact some cultures are particular prone to it. For example the old joke “If you have three Jews you have five political parties!”.
Our system basically breaks (and I don't mean breaks down!) out politically along one fault line - Centralized government vs Decentralized government. It doesn't matter what the parties are currently called now but they battle over that issue. In fact the Rats were once the party of decentralization and the GOP the party of increasing federal power that has more or less switched. Third, 4th & 5th, etc parties always form around a single issue. If the issue is meaningful in any way to the electorate it gets absorbed into one of the two dominate parties. The fringe party then fades into obscurity. For example the GOP with the help of the Civil War absorbed the Whig party. Historically it has always worked that way.
No sooner was Washington in office it started happening - Federalists vs Anti-federalists. They didn't quite call themselves that then but within 10 years they pretty much did. (And historians do now!) Federalists - Washington's faction even though he would likely deny he is a member of it. These factions\parties consisted of those who were supporters of a strong centralized government. Hamilton the most famous of that group. (There are others you can look those up!). Jefferson the obvious example of the anti-federalist group. Every political issue since then eventually devolves down to the question of how much does the federal government get involved in the states and its citizen's lives. The Civil War is the most noted example of that issue where it couldn't be resolved except by violence - and some of those states rights-vs Federal powers issues still aren't resolved. The Great Depression is another example of the Federal Government imposing centralized solutions - bad solutions. Other examples of Federal centralized power expanding at the states expense is the 16th and 17th amendments. I view the 17th amendment as the more damaging of the two. It took the states out of the role of directly influencing federal policy. Turned the Senator into a “Congresscritter-at-Large” his\her states interests took a much lower priority, the highest priority was returning to office. This made the senator far far more receptive to national party politics. Why she\he needed the money streams for reelection from the national party.
There is no way of preventing political parties/factions from forming. Like I said in the first paragraph its human nature. Do you want to pass a law forbidding this act of "freedom-of-assembly\association"? Hasn't "freedom-of-assembly\association" been abused\curtailed enough by feel good civil rights legislation is the last 60 years? Somehow forcing mutiple parties onto our system will do nothing more then fragment politics further and cause even more rancor and stagnation. I admit sometimes poltical stagnation is appropriate but not as a first choice.
Multiparty system work “best” (and its a qualified “best”!) in a parliamentary system. Ours is NOT a parliamentary system! Our system is a sort of “winner-take-all” executive system and made that way by the Constitution.
A multiparty system here would mean some form of coalition politcss in the national and state legislatures. However unlike parliamentary systems elsewhere you would have no way of incentivising your coalition with national\state ministries to run. In the UK the PM (an MP elected only from his bourough & not the nation!) hands out ministries like defense, exchequer, foreign office, etc to other MPs and\or party honchos. That all sounds pretty self-centered if not a bit corrupt. However that's how it works there. I don't see it as an improvement. It's not going to change unless the Constitution is radically changed. I don't want that!
The way I heard it, "two Jews marooned on a desert island have to build three synagogues. One for the Reform, one for the Conservative, and one neither one would be caught dead in."
--- "Our system basically breaks (and I don't mean breaks down!) out politically along one fault line - Centralized government vs Decentralized government."
Agreed. Towards liberty and away from pervasive rule, as opposed to towards great rule and away from liberty.