True, and we don't have much to go on. Since the base coin is Spanish colonial, we can exclude the political protest of an angry Portuguese, who didn't like the Spanish takeover of Portugal. If the stamp is Iberico-colonial, the most likely areas are where Portuguese and Spanish interests met, i.e. East Asia and Brazil. Brazil was a rich colony, in no need of silver coins from Bolivia, so if the counterstamp is from there, chances are that it is a private political protest. The die is professionally done, so I'd suspect a local jeweller.
In East Asia, the Spanish takeover could have cut off the flow of Portuguese coins to its established colonies. Silver from Bolivia was transported to Veracruz by donkey power, hence to Manila with the Manila galleon and from Manila it could have gone anywhere. Therefore, the counterstamps may have been applied officially in any Portuguese settlement in East Asia and chances are that it would be an emergency measure (though a political protest is hard to exclude here also). I'd find it hard to explain that Spaniards would counterstamp their own coin, even harder to explain why a silver coin would be countermarked with a symbol from a gold coin.
Peter