Add blackberries, mint, lemon juice from one wedge and lime juice from one wedge to tall glass.
Muddle with a muddler until blackberries are crushed.
Add rum.
Add ice to almost fill the cup.
Fill glass with club soda. Mix thoroughly with a straw, stick, or spoon.
Garnish with lemon, lime, and fresh blackberries.
Notes
We use regular granulated white sugar, but some may prefer to use simple syrup in its place. To do so, simply sub the granulated sugar for 3 teaspoons simple syrup.