Is there any way for Mexico to take Cuba, Santo Domingo, Puerto Rico and the Phillipines with it into independence as the Empire of Mexico? And what would the result be?
The most likely result would be a short-lived claim as Mexico wouldn't have the fleet and the troops to enforce it.
Considering how well it went with the northern territories, it's going to be hard to enforce the claims, with Cuba and the Caribbean going independent if given along with the independence. Unless Mexico gets a stable government instead of the musical chairs it had, or goes Dominion (though, that's a very dim possibility).