China Airlines brought me from Los Angeles to Hong Kong, Bangkok, Jakarta, Bali, and back to Los Angeles. Fortunately, the price is unchanged. There are three things you need to be aware of before purchasing your ticket. If you like for example United Airlines, check to see if they fly to your destination. However, you might find that United charges more than other airlines, so your purchase might depend on the price rather than your original preference.
Most airlines have a 'home city' their planes have to use for stop overs.
So, if you use the Russian Aeroflot, you have to land in Moscow, even though this increases the flight distance. Sometimes, you get caught up in a place and want to stay longer. That pushes all your departure dates back, so it could get expensive. Remember to check if you can change the ticket at all after you've paid for it. Finally, it might be cheaper to buy a return-ticket to a single destination, and then purchase tickets from there to further destinations.