United States of Bolivia-Peru that forms after after a Pacific War draw. Follow it up with a Evo Morales type figure coming to power and incorporating successfully rebellious Mapuche.
There is an historical one used by the Peru–Bolivian Confederation (1838-1839) which appears to have combined both countries' arms in a wreath on a red field (a number of differing reconstruction can be find online). Maybe it would have been readopted or at least a variant of it might have been.