Preheat the oven to 300°F. Crumble up the chocolate graham crackers, mix them with the melted butter, press the mixture into a springform pan, and refrigerate the pan while you prepare the rest of the cake.
Make fruit purées from the fruits listed above. To make the purées, cook each fruit separately with water and sugar and let simmer for 2 to 3 minutes. Then use an immersion blender and blend until smooth. Once done, let the purées cool completely.
In the meantime, mix together the cream cheese, eggs, sugar, flour, corn starch, and butter for the cheesecake batter. Pour half of the cheesecake batter into 5 equally-sized bowls and add one fruit purée to each bowl.
Remove the springform pan from the fridge and start layering the batters. First start with a ladle of the plain cheesecake batter, followed by a ladle of the strawberry-flavored cheesecake batter, followed by another ladle of the plain cheesecake batter, followed by a ladle of the peach-flavored cheesecake batter, followed by a ladle of the plain cheesecake batter, and so on and so forth until you make your way through all the colored batters. For best results, use each color about three times.
Bake the colorful cheesecake in the oven for about 60 minutes.