If you're coming into EZE on BA (the 247 I take it) and are thinking about tier points, you might try "breaking" the journey in GRU (plane lands there anyway). Usually I do this by making a 1-2 day stopover there, although last time I accomplished the same thing (tier point-wise) without getting off the plane... I had originally planned my usual day or two stop, and as such I was ticketed with a stop in GRU (and therefore separate e-ticket coupons for the two legs of BA247). When it turned out I had to go straight through, I was able to reschedule these to the same day (same flight and a/c, really) but still have it issued/checked-in/credited as two flights. Which, owing to the way this 5th freedom flight from GRU-EZE is credited (as though longhaul), essentially gets double tier points.

The logistics have potential for issues if you're actually going straight through, so it's more obvious if you just break the trip with a day or two in Sao Paulo. If going straight through, though, I'd recommend OLCI'ing for both segments ahead of time, and then once onboard, in my case (in F) the CSD quickly sorted out that they could just have someone take my BP out to the gate, scan it in, and bring it back to me. I wouldn't count on it working seamlessly this way every time, but the worst that could happen is you have to get off, go through connections and back to the gate, and get back on again.