TORONTO (Reuters) - Canadian stock trading volumes look set to rise in the coming months as the country's main stock exchange and its domestic and foreign competitors push to roll out new dealing platforms and fresh ways to route orders.

The changes, which some warn could inflame tensions over trading costs, are part of a global trend that has seen traditional exchanges and new players fight aggressively for market share.

"There's the possibility if there's real innovation out there you'll see some more growth," said Thomas Kalafatis, head of prime brokerage and securities lending at CIBC World Markets.

"That's why the industry looks at volume as one of its key metrics because it shows that your output ... is being enhanced. There are still plenty of unmatched trades happening. The challenge of the marketplace is to make the match."

Canada trades an average of around one billion shares a day, the majority of them on the Toronto Stock Exchange and TSX Venture Exchange, both of which are owned and operated by TMX Group Inc.

But TMX has come under pressure in recent years from Alpha ATS, an alternative trading system backed by the investment dealer arms of Canada's big banks.

TMX's exchanges accounted for nearly 75 percent of total stock trading share on a volume basis in September, while Alpha made up about 17 percent, according to data from the self-regulatory body the Investment Industry Regulatory Organisation of Canada.