Thanks bingocallerb22 - I did find that section, but I couldn't tell if it only applied to oneworld awards or not. Hopefully I don't have any problems booking.

just to add my one cent. Open jaws and stopover are permitted unless the trip includes Iberia segments. I have no idea the logic behind this, but it's how it works.

On the other side you CAN see availability and book OW award flights even if there are no segments operated by LAN in your itinerary. The page doesn't work too well... even if there are, let's say 10 flights, on a route per day, the page will show you only the first ones of the in some occasions. To get to this point just put your origin and destination on the award search engine, you will end in a page saying that LAN doesn't fly the route but press the link to look for oneworld availability.

Finally I think availability is the same that all OW airlines get on their partners, not better and not worse. Just as shown by ITA when searching for award trips.

I need a double open jaw but the agents do not allow.
Unlucky.