Coalition governments are possible in Canada, and have occurred before. In the case of the last election, the votes were split such that the Conservatives won a majority of seats.
It seems though that it only may be possible at election time. A few years prior to the election in which the Conservatives gained a minority, the Liberals and the NDP attempted to form a coalition government and the Governor General (The queen's representative in Canada) ended up proroguing parliament on Stephen Harper's behest. https://en.wikipedia.org/wiki/Prorogation_in_Canada#History
