The growth potential for Tim Hortons seems limited in my opinion -- it will continue to fill each corner of Canada, but we already know that and this is priced into its existing valuation. It dominantes Canada but that is because it is seen as part of Canadiana. It's attempts to expand into the US have generally not succeeded.[1]

Both are already large enough to have economies of scale in terms of purchasing power, thus I do not see the reason for this outside of tax savings.

Strangely, a lot of Tim Hortons in Canada share buildings with Wendy's. Thus there is some cross pollination there between these two, maybe the strategy is to take this to the extreme and have nearly each Tim Horton's location be paired with a Burger King.

BTW some of the richest people I know (10,000 sq ft homes) own Tim Horton franchises (usually in central locations in major cities.) A boring business compared to startups, but damn it can be crazy profitable. Might be the time to snap those locations up if they are going to do some major US expansion.

[1] See https://en.wikipedia.org/wiki/Tim_Hortons#Northeastern_US_de... But another commenter disputes that and he may have more recent information.