A multi-party system with fractures parliaments isn't the solution and likely to lead to instability with months or years of difficult government formations. Look at Spain or Israel, where current governments are de jure just "acting" for months or years. I wish Germany had a two party system with conservatives and left-liberals as main competitors and a majority vote like the US and UK.
The US has had a malfunctioning government for the last decade even without factions, so that's not something a two party system would prevent--if nothing it worsens it.