Make the basil syrup: Bring the sugar and 1/3 cup water to a boil in a small saucepan, stirring to dissolve the sugar. Stir in the basil, then remove from the heat and let cool completely, about 1 hour, then strain.
Muddle 3 plums in a large liquid measuring cup with a wooden spoon. Stir in the basil syrup and gin. Refrigerate until ready to serve. Pour into ice-filled glasses and top with the seltzer. Garnish with basil and the remaining sliced plum.
Photograph by Con Poulos