Place plums in a medium bowl. Pour brandy over plums. Cover and let stand overnight. Drain.
Let plums stand on paper towels for 2 hours to drain thoroughly. Line a baking sheet with waxed paper; set aside.
Meanwhile, in a medium bowl combine butter and corn syrup; stir in powdered sugar. Knead mixture until smooth (chill if mixture is too soft to handle). Shape about 1 tablespoon powdered sugar mixture around each plum. Roll in palms of hands into smooth balls. Place coated plums on the prepared baking sheet. Chill for 1 to 4 hours or until firm.
In a medium heavy saucepan melt candy coating and bittersweet chocolate over low heat, stirring constantly until smooth. Line another baking sheet with waxed paper. Using a fork, dip plums one at a time into melted mixture, allowing excess to drip off. (Be sure to completely seal plums in melted mixture to prevent juice from leaking.) Place coated plums, on prepared baking sheet. Chill until the coating is set (1 to 2 hours).
If desired, line another baking sheet with waxed paper. Place about 2/3 of the milk chocolate in a small microwave safe bowl. Microcook on 30 percent power for 1 to 1-1/2 minutes or until chocolate has started to melt (110 degrees F on an instant read thermometer). Add remaining chopped chocolate; stir until melted and smooth. (Temperature of the chocolate will drop to about 85 degrees F.) Reheat as needed for 10 seconds on 30 percent power. Dip half of each candy into the melted milk chocolate. Place on prepared baking sheet to set.
Store, tightly covered, in the refrigerator for up to 1 month. Makes 20 to 22 candies.