Originally Posted by Pseudo Nim

Without a doubt, you should not use Aeroplan for stops inside Japan. You should get an Amex card, get some Membership Rewards points, convert them to Avios and use Avios for intra-Japan flights on JAL (4,500 each way), so a single signup would cover two round-trips for two adults pretty much anywhere in Japan. Alternatively, they sell flight passes for 10,000 yen which have several segments built in (called Explore Japan or something like that) but it depends on where you want to go. Incidentally, why only NGO and CTS? I'd advise to include at least one of the major cities like Kyoto if it's your first time in Japan, just because it's something you absolutely must see -- but I digress.

To stop by Europe, you'd need to make your destination somewhere else in Asia first. Unfortunately both Bangkok and Singapore have moved to Asia2; but the point difference is not stupendous, so you should consider booking to those destinations - that would permit a stop in Europe. So you should be able to do something like YYZ-CPH, CPH-(xxx)-(SIN/BKK), (SIN/BKK)-NRT, NRT-YYZ. Inside Japan, you would do HND-NGO, NGO-CTS, CTS-HND and then fly back. It's highly unlikely you can get ALL flights onto a single ticket - but to be honest, I've not checked routes into Nagoya from Asia (but I think there's a flight back to Canada from NGO? I seem to recall AC advertising it). So maybe you could do BKK-NRT (or HND), then HND-NGO, NGO-YYC-YYZ or something like that.

But do consider the flight pass or the Avios options for inside Japan.