Add the blackberries, mint, juice of 2 limes and agave to a pitcher and muddle until the blackberries release their juices and the mint is fragrant.

Stir in the white rum and wine and slice the remaining two limes to add to the pitcher.

Let the sangria sit in the refrigerator for at least an hour before serving.

When ready to serve, fill the pitcher with ice and top with club soda.

Serve in glasses garnished with additional mint leaves and blackberries.