As Kiwi Flyer has mentions, not all that many options for South America.
Note that there are a few types of RTW fares. There are the standard alliance offerings from OneWorld and Star Alliance, which provide maximum flexibility and coverage over their entire alliance routes. Then there are special deals offered by specific airlines, which are often less expensive but more restrictive and sometimes short-term special deals.
To include South America, you are likely to be restricted to the standard OneWorld or Star Alliance RTW products.
The cheapest way to buy the OneWorld RTW products (OneWorld Explorer and Global Explorer) is to call American Airlines directly, and ask for the Round the World Desk. The base fare cost is always the same (between calling an airline directly or using a travel agent), but AA do not include the fuel surcharges that are often added by other airlines. And the AA RTW desk is very knowledgeable and efficient when it comes to the OneWorld products.
Kiwi Flyer can provide more info on the Star Alliance RTW products, which I understand are more like the OneWorld Global Explorer, being mileage based. The OneWorld Explorer is based on the number of continents visited.