I wonder - in the UK we have a pseudo-two-party system. There is significant influence from other parties, but there are only two parties which could ever form a government, or lead a coalition. Other countries with systems very similar to ours have more genuinely multi-party systems where at least three parties have the possibility of leading the country, or making up a major proportion of the government (it helps when you have certain areas where a fairly small minority party can form a majority), like India and Iceland
Parliamentary democracy and proportional representation tend to select for such systems, and don't lead to the level of divisiveness that you folks are getting into.