How could Portugal have colonies in the Caribbean?

Is it possible to have colonies in the Caribbean and still maintain the territory that you have gained from Spain besides the tordesillas treaty in present-day Brazil?
 

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Portugal (along with Spain) had a claim to Barbados for roughly a century prior to the beginning of English settlement of the island in the 1620s. Perhaps Spain colonizes the island sometime in the mid-1500s, and then Portugal takes it with them after the Iberian Union is dissolved.
 
Portugal (along with Spain) had a claim to Barbados for roughly a century prior to the beginning of English settlement of the island in the 1620s. Perhaps Spain colonizes the island sometime in the mid-1500s, and then Portugal takes it with them after the Iberian Union is dissolved.

1620s were when Portugal were part of the Iberian Union, yes, which is probably why England colonized it. How can the claim be respected and better yet, Portugal plants Luisitanian ass on the island?
 
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