In Germany we have a multi-party system and it works a little better than in the US but it's not a silver bullet either. After each election, the elected representatives vote for our chancellor (similar to the American president). Because we have so many parties and the two largest parties usually get only 20% to 40% of the vote, they need to form alliances with the smaller parties in order to gain a governing majority.
Sometimes our conservative party will team up with the liberals, sometimes our social democratic party will have to team up with a right-leaning party and sometimes the two big parties will even form an alliance.
This works fairly well, especially because each state government has a different set of governing parties so there's not as much bitterness and more people get to work together. That said, within each office, parties still consider themselves to be either governing or the opposition and fall into opposition mode for a few years, just like they do in the US.
Sometimes our conservative party will team up with the liberals, sometimes our social democratic party will have to team up with a right-leaning party and sometimes the two big parties will even form an alliance.
This works fairly well, especially because each state government has a different set of governing parties so there's not as much bitterness and more people get to work together. That said, within each office, parties still consider themselves to be either governing or the opposition and fall into opposition mode for a few years, just like they do in the US.