You're allowed only 1 stopover (+24hrs) in a city per itinerary, but you are allowed a further two transits (-24hrs) of the same city in one itinerary. The clever ones among us get creative and book a early afternoon arrival with a morning departure next day to stay under the 24hr limit, but getting you an extra night in the same city again.

As for Sth America, you can get there via Europe in one direction, but to get back here, then yeah, you still need to go via Nth Am. (Unless RG want to start a service to PPT to link with NZ, it will probably stay that way!).

However, there is one "loophole" to this which is either a plus or a minus pending your point of view!! You can legally go around the world via Asia twice, without even seeing one drop of the big Pacific Blue. Mapleflot's DEL-YYZ nonstop service is trans-pacific, giving you the one obligatory Pacific "crossing". A SYD-SIN-BKK-DEL-YYZ-Nth/Sth Am-Euro via Atlantic-BKK-SIN-SYD is legal. So although it still involves a transit via Nth Am, you don't have to go over the Pacific through Nth Am to get into Sth Am.