Since it includes South America it would be a four continent fare, as in LONE4 (Europe/Middle East, Asia, North America, South America.)

Current pricing for ex-USA is US$4999 plus taxes and fees. Ex-Brazil it's $4069+. For what it's worth, ex-Canada it's $4089+. If starting in, say, Toronto, your friend could end anywhere in North America.

So for example, the route could be something like this: YYZ-xMIA-GRU-DOH-SIN-HKG-LAX-RDU.

If your friend has flexibility in timing the stops, then the LONE4 price originating in London is quite a lot cheaper - $2805+ - and would come with the advantage of allowing stopovers between each of the six allowed North America segments. If originating in N. America you're only allowed two stopovers.

Of course that would mean altering the route, possibly with an east-to-west direction instead of west-to-east, e.g. LHR-MAD-GRU-MIA-RDU-LAX-HKG-SIN-LHR. Or if the S. America stop could be timed after the Asian one(s) then he/she could take full advantage of the N. American segments before ending back in Europe, e.g. LHR-SIN-HKG-xDFW-GRU-DFW-ANC-PHX-YVR-JFK-RDU-MIA-LHR. Note this last route takes advantage of the rule allowing a transit through North America between Asia and South America without violating the "single entry" rule which restricts entering the same continent twice.