Spray a deep dish 7 inch springform pan with nonstick cooking spray. Line the bottom of the pan with parchment paper for easy removal of the cake once it’s done.
Cream the cream cheese with a handheld mixer on low speed until very smooth, scrape the bowl and mix again. Add sugar and cornstarch; continue to scrape and mix the ingredients together on low speed.
Divide batter into 3 separate bowls. Melt the milk chocolate in the microwave for 30 seconds, stir. Return the chocolate to the microwave for another 15-30 seconds.
Whisk into one of the bowls of cheesecake batter. Repeat with the white and dark chocolate. Refrigerate the 3 bowls for 15-20 minutes so they will be more firm for layering.