Yep.

Europe:
#1 lon-bey
#2 bey-lon
#3 lon-osl
#4 osl-lon
#5 lon-bcn

South America:
#1 gye-scl
#2 scl-lim
#3 lim-scl
#4 scl-ccs
#5 ccs-scl
#6 scl-eze

Three extra segments.

Just a few more comments. You can go mel-hkg-dps on Cathay without extra charges. CX biz is pretty nice. If you are doing this primarily for miles, you could do bcn-(scl)-gye-(scl)-lim-(scl)-ccs-(scl)-eze. Personally, I wouldn't do either. Without debating whether to use IB, since I have not flown them, I would probably go bcn-(scl)-ccs-(scl)-gye-(scl)-eze. I would for two reasons. First, it cuts one segment charge off. Second, if you want to downgrade the additional sector to coach, it is on the shortest sector.

Have a good trip. Don't expect the Lan Chile miles to post any time after flying them. Loved the airline, but miles posting has been like pulling teeth from an alligator. So far, AA has been useless, other than to say that I need to wait a full 60 days.

If they serve the Tarapaca Millennium in biz, drink a glass or 6 for me....