Speaking as someone who actually lives in a bastardized version of a parliamentary democracy that seems to function as a republic more days than not, I think those of you advocating for the third party protest vote really are missing the boat here.
Canada presently has 3 major political parties - a "right"-wing coalition currently called the Conservative Party ("right" is in quotes as they're about on par with the Democrats in the US most days), the Liberal Party (fiscal right, social center), and the NDP (leftist). In the last election, the Liberals were nearly obliterated, the NDP got official opposition, and the Conservatives took a majority stake.
It hasn't always been thus. In the 1980s, the then-Conservatives (a different faction altogether) imploded and became three parties: the Conservatives, the Reform, and the Bloc Quebecois. The led to a decade of Liberal rule with the NDP in a small minority stake. When the "right" reunited under the Conservative banner again and the Bloc lost traction, it flipped. This last election was the first time the NDP took any major ground and it was all taken at the expense of the Liberals and the Bloc.
So where is Canada today? More or less the same place - politically - as we were in the 1990s. Two major parties positioned on opposite sides of the political spectrum (which is a very small spectrum in this country anyway), with tiny parties in the fringes with virtually no clout.
Don't expect party implosion or third-party votes to substantially change things. Unless your government structure includes a form or proportional representation, virtually all democracies end up with a two-party state in practice in not fact, and those who influence power behind the scenes will line up behind one, the other, or both as they always do. Who the two parties are changes very, very little.