We have a multi-party system here in The Netherlands. [Edit: I slightly misread your post.] Here, some people may vote that way yes, having a preference for a further-off-centre party, but voting more centre so "their" party might be able to form a government. That's what we call strategic voting in a multi-party system, but it works a little counter-productive, and people are starting to see that more and more. Because when people are giving their vote to smaller, further-off-centre parties, the bigger centre parties need to align with these further-off-centre parties in order to get a majority and form a government. If the big centre left party is losing votes to smaller more left wing parties, it becomes more attractive to work with them than with the big centre-right party, and vice versa for the right, of course. So you're generally better off voting for what really suits you best.
We have a proportional representation system where the government needs at least a minimal majority in the House. What you get is compromise politics. Neither left nor right get completely what they want, so it's basically going pretty centre. Sometimes more social, sometimes more liberal (economically speaking), but there's at least continuity. There's not a lot of governments trying to completely undo what the government before it did. Of course there's drawbacks too. Sometimes the results are very evenly spread and forming a coalition can become problematic when there are polarizing issues on the agenda. As far as I know there's never been a single party government, it's always been coalitions from 2 to 5 parties, I think. Sometimes a brittle coalition with a minimal majority is formed, and just one person breaking with the party/coalition line will result in the loss of a seat, and thus the majority needed to govern. We've frequently had government crises, which happens when parties (we call them "fractions") within the government cannot reach a compromise on some pivotal issue. But that just means slightly more frequent elections, which is not necessarily a bad thing. It's not perfect, but it seems healthier than the two party deadlock phenomenon in the US.
You really have to wonder what it will take to break out of that 'binary' system.