Here's the definitive Globe and Mail article on the subject. The Blue Jays want to install natural grass in the Dome and that precludes the Argos from playing there. I assume that for Grey Cups, the grass is removed at the end of the baseball season and thus Grey Cups in November can be played there.
So the Argos have to find a new home. MLSE has already mulled buying them and having them play at BMO Field. The Argos could play their potentially 11 games a year there on the natural turf without too much damage (rugby is already played on it), however MLSE could put back in artificial turf. That could make CFL haters the Red Patch Boys and former Toronto mayor David Miller* crazy, however Toronto FC has sucked its entire existence, but with and without grass. As I already mentioned in another post, having the Argos play at BMO on national television would boost the value of the naming rights.
Potentially the Argos could try an ultra cheap bare bones stadium somewhere or other. Really the Argos need a small stadium around 20,000 seats they can fill and the CFL needs the television money. People will watch the Argos on television but they won't watch TFC. Maybe the Argos could partner with the rugby and cricket folks for a stadium.
One thing to consider with television is that the CFL needs the Argos. They may be willing to fund $5 million per year over 20 years to help with a new stadium. Perhaps the Argos could partner with a developer and have some condo towers integrated with the stadium and get some money that way. This issue will probably simmer for a few years and then heat up.
*At least current Toronto Rob Ford is a CFL supporter, even showing up at a game in Saskatchewan.