Cut two of the limes in half, and cut the third lime up into wheels, throwing out the end pieces.
Using a citrus press or other juicer, juice the four lime halves and place the juice into the pitcher.
Add the pineapple juice, simple syrup and water or seltzer into the pitcher.
Add ice to the pitcher and stir together with a long spoon.
Add several lime wheels to the pitcher. Fill your serving glasses with ice and lime wheels, and pour the drink into the serving glasses. Serve immediately.
If you are planning to make this in a large batch that will sit outside, a great idea would be to make a batch ahead of time and freeze it into ice cubes. Use those cubes for half of the ice that you put in the pitcher. That way, it won't get as diluted as the ice melts.
Notes
You can substitute an equal amount of honey for the simple syrup, or use 2 tablespoon of sugar (preferably superfine/caster sugar, so it dissolves quickly). You can also use a sugar substitute like allulose.