I think you can extend your stay in Canada as many times you want. I think the Cap a person can stay in Canada is 1 Year. I don't think the TRV will be extended from here. Only a Visitor Permit will be made available for his stay.
My personal opinion would be to ask your dad to travel back to home country before the TRV expires as that is good for his future travels and applications. There are chances in future that they may question about why he overstayed in Canada when his TRV was expiring. It may also raise doubts during future immigration that why did he overstay.
hence I would advice to go back and apply in home country and return back. I know there is a cost and time factor associated with it, but doubts raising in future immigration and travels to Canada is more risky.
That is my thinking, I may be overthinking or over analyzing the situation but its my own personal opinion. Have watched a lot of Border Security shows, hence this kind of thinking.