Round The World (RTW) fares are still very good value for money and especially, in business class.
Recently, I had to produce an itinerary which covered Las Vegas and Shanghai; just two stops. If I arranged this as flying London > Las Vegas > Shanghai and back via the US, then the cost in business would have been a shade over £20k. Quite a tidy sum.
This should then be compared to what it would cost, if one simply kept going. The price then becomes £6,100-ish.
There are additional benefits. You could stop many more times, should you wish to do so, in fact you can have up to 16 segments on the One World RTW thrown in for the same price. You have to be away for at least 10 days, cover 3 continents and not take longer than a year over your journey. You can cross the Atlantic and Pacific only once (each) and you have to keep going in the general direction of East or West. That is a very simple summary of the rules, there are other bits, of course, but certainly with One World, changes are within the bounds of possibility. That said, it always pays to try to keep to your itinerary, once booked.
You need to check on visas and such things as ESTA's, of course and make sure that you have adequate insurance cover for a global trip.
The Star Alliance also have a similar programme. Which alliance you choose rather depends on the trickiest part of your itinerary. Not all airline partnerships cover all destinations. One World, in the shape of British Airways, fly directly from Shanghai to London, Star Alliance do not, so your return would need to be on Swiss via Zurich or Lufthansa via Frankfurt.
You do not have to decide right away. Travel Agents will happily hold an itinerary for a while, quite a while, in fact. This is helpful as many of these RTW trips tend to evolve, rather than get booked as a "decide and ticket" arrangement. Although there are online tools to book RTW tickets, an airline reservation system equipped traditional travel agent - or business travel agent - is the best place to start.