Halve and pit plums. Whisk the sugars and water together in a small saucepan. Add the plums and simmer over medium heat, until tender but not mushy, about 10 minutes. Cool plums in the liquid.
Slice half a plum for garnish and set aside.
Put the diced limes and remaining plums in a large open pitcher. Crush thoroughly with a muddler or a potato masher (it works great). Add cachaca and the plum cooking liquid and fill with ice cubes. Pour into chilled rocks glasses, allowing some ice and fruit to fall into the glasses as well. Garnish each drink with a slice of poached plum.
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