In a large bowl, combine the cream cheese and sugar and mix on high speed with an electric mixer until light and fluffy.
Separate the mixture in three equal portions and transfer them in two other medium bowls. (In total having three bowls).
Melt all three kinds of chocolate in separate small three bowls and add each melted chocolate in different cream cheese mixture to obtain three bowls with three different chocolates mixtures.
Whip up heavy cream (whipping cream) until stiff peaks form. Separate the whipped cream in three equal parts and delicately fold in the separate three chocolate cream cheese mixtures.
Pour the first dark chocolate into reserved Oreo crust and spread evenly all the way to the side of the pan. As a second layer, pour the milk chocolate cream cheese mixture and spread as well delicately all the way to the edge of the spring-form. Repeat with the white chocolate cream cheese mixture, smooth the top with spatula.
Cover the spring-form pan with plastic food wrap and place it in the freezer to set. For 4-6 hours.
Remove the cheesecake from the freezer and place damp hot kitchen towel around the spring-form, to release easily the sides.