I have just ticketed Chicago-Santiago Chile (stopover for a few days)-Buenos Aires(destination for a few days)-New York(stopover for a few days)-Chicago all for 60,000 miles. Let's see if this gets ticketed, but two reservations people have looked at and no one has said anything to the contrary.
I am curious if the stopover is not allowed, perhaps a 100 dollar change fee will let you take any given flight earlier than booked, thus making it a stopover.