The start and end of the journey almost always have to be located in the same country and exactly one crossing each of the Atlantic and Pacific must be included in the itinerary.
It is possible to piece together a round-the-world route by combining one-way tickets on various airlines without resorting to alliances.
These can be found in major cities that are transit hubs — San Francisco, London, New York, Bangkok, etc.
Travel agents may get parts of tickets issued by contacts in other countries, and often use pre-arranged contractual agreements with various airlines.
It is important to have long waiting time between such flights, preferably a hotel night, which gives the chance to see one more city.