1. Line a 9- x 5-in loaf pan with parchment paper, leaving an overhang of 3-inches on the two long sides. Place all but 1/4 cup of the raspberries in a small bowl and mash with a fork. Push the mashed raspberries through a mesh strainer into a bowl, discarding the seeds. Stir 1/4 cup powdered sugar into the mashed raspberries.
2. In a large bowl, using an electric mixer, whip the cream, remaining 1/2 cup powdered sugar, and vanilla to medium-soft peaks. Reserve 2 Tbs. of the raspberry puree for serving then fold the remaining puree into the cream.
3. Place 3 to 4 ice cream sandwiches in bottom of prepared loaf pan, cutting to fit. There will be some room on the ends of the pan. Spoon one third of the cream mixture on top, spreading until smooth (some will settle in the gaps at the eds of the pan). Repeat layers, two more times, using 4 ice cream sandwiches crosswise on the final layer. If desired, transfer remaining cream to a large piping bag fitted with a star tip and pipe rosettes on final layer. Freeze until firm, at least 4 hours. To serve, spoon over reserved raspberry puree, reserved raspberries, and fresh blackberries, blueberries, and strawberries.