Preheat the oven to 325°F (163°C) and grease a 9-inch springform pan.

Combine the chocolate cookie crumbs, 1/4 cup sugar, and melted butter in a mixing bowl and press into the bottom of the prepared pan.

In a medium saucepan, heat the sugar over medium heat, stirring constantly until it melts and turns amber, then add butter and heavy cream to make the caramel.

In a large bowl, beat cream cheese with 1 1/4 cups sugar until smooth, then add cocoa powder.

Add eggs one at a time, mixing well after each addition, then stir in sour cream and vanilla.

Divide the cheesecake batter into three bowls and mix in the melted chocolates.

Pour semi-sweet chocolate batter over the crust, then layer in milk and white chocolate batters.

Drop spoonfuls of caramel over the batter and swirl gently.

Bake for 1 hour and 15 minutes until the center is set but slightly jiggly.

Turn off the oven, leave the door ajar, and let the cheesecake rest for 1 hour.

Cool to room temperature, then refrigerate for at least 4 hours or overnight.

Prepare ganache by heating cream to boil, then pour over chopped dark chocolate and stir until smooth.

Pour ganache over chilled cheesecake and allow it to cascade down the sides.

Garnish with chocolate shavings, caramel drizzle, and fresh raspberries if desired.