Line a 9-inch square baking pan with plastic wrap. Brush a medium bowl with butter. Add 2 1/2 cups cereal, 1/3 cup raspberries, and 1/4 cup blueberries to bowl; stir gently to combine.

Melt 2 tablespoons butter in a medium saucepan over medium-high heat. Add half the marshmallows and cook, stirring, until melted, about 1 minute. Pour into bowl with cereal mixture; stir gently to combine and evenly distribute berries. Press cereal mixture into prepared pan in an even layer. Freeze until chilled, 30 minutes.

Transfer ice cream to refrigerator and let soften slightly, 20 to 30 minutes. Spread in an even layer over cereal mixture. Freeze until firm, about 1 hour.

Place remaining cereal and berries in same bowl. Melt remaining 2 tablespoons butter in same saucepan over medium-high heat. Add remaining marshmallows and cook, stirring, until melted, about 1 minute. Pour into bowl with cereal mixture; stir gently to combine and evenly distribute berries. Drop spoonfuls of cereal mixture over ice cream, pressing gently to fill gaps and create an even layer. Cover with plastic and freeze until firm, at least 2 hours and up to 2 days. To serve, remove plastic, lift from pan, and use a serrated knife to cut into 12 squares.