People who complain about the 2-party system in America have no idea just how much a multi-party system can suck. Americans think in a multi-party system, they will have choices that are much different from the Dems and Repubs in some crucial ways such as being beholden to lobbyists and corporate interests. IMO, it's a naive expectation. Politicians are politicians, regardless of what party they belong to.

I am originally from India, and this is what happens in an Indian multi-party system:

1. In most elections, the votes are distributed so much among the various parties that no one party has enough of a majority to form the government. Usually, the party with the highest seats won tries to stitch up a coalition in conjunction with a few other parties so that together, they have enough seats together to form a majority. Many times, another party which does not have the highest number of seats won can still partner up with a few parties and end up with a majority total. This is called a coalition government.

2. When the government is formed by multiple parties, it is pulled in multiple directions. It has to take into account multiple ideologies and interests. As a result, there is often deadlock in the functioning of the government and they do not get much done at all. It is a miracle how they manage to get even a little accomplished.

3. Sometimes, a group of parties lack just a few winning seats to form a majority. Say, 2-5 seats. They manage to convince a small party which has won just 2-5 seats to help them form the government. Now, this small party knows that it has the power to make or break the government. If it pulls out of the government, the ruling coalition will lose the majority and won't be able to rule any more. So, this small party ends up blackmailing the government to get enormous sops in its favor. It becomes a case of the tail wagging the dog. These small parties can hold a whole nation's stability and progress to ransom for their petty demands. This happens way too often.

4. In a multi-party system, there are often parties which are focused on regional issues. These parties are not really interested in any major national issues. Yet, they field candidates in national-level elections. And since regional parties tend to be popular in their respective regions, many of them end up winning seats in the national-level elections. When major parties want to form a coalition, they end up incorporating these regional parties to make up a majority number. Once again, these regional parties and their narrow interests have disproportionate influence on the functioning of the government. They force the national government to focus on regional issues, at the cost of national issues being abandoned. Can you imagine the political stability of an entire continent-sized nation being threatened by some regional issue that is going on in one individual state?

I am from a multi-party country and I am here to tell you that it is a multi-ring circus. It would be so entertaining, if it did not play such havoc with the country's progress. People in many countries with a multi-party system actually admire the US's two-party system.

Edit: I understand that there are many countries which have a more efficient multi-party system in place. However, I don't know how this will play out in the US. In recent years, the US government has proved itself to be inept at getting things done due to the conflict and gridlock between two parties. I am not confident that this situation will get better in the US if multiple parties participate in these conflicts and gridlocks.