Unfortunately, since the market has been deregulated and Air Canada is a private company, it would be difficult to take markets away from it. That would have been possible when it was a crown corporation.
From 1937 until the 1950s, the airline industry started to expand and the market was not very competitive. Air Canada took advantage of the fact that the government had set aside some market shares and routes for them; it gave it priority in this area. Now that it is a private company, it is the market that dictates which routes are taken up by one company or another.