In large bowl, combine the crumbs, sugar and butter; press the mixture onto the bottom of a 9-inch springform pan, and bake the crust for 10-15 minutes, or until it is set.
In the bowl of an electric mixer, beat the cream cheese until it is smooth and add the eggs, sugar and sour cream, beating until the mixture is combined well.
Divide the mixture among 3 bowls and set the bowls aside.
In a double boiler, melt the white chocolate, stirring until it is smooth. With a hand-held mixer, beat it into one of the bowls of cream mixture until just combined.
Melt the milk chocolate in a double boiler. With the hand-held mixer beat it into one of the remaining bowls of cream cheese mixture until just combined.
Melt the semisweet choclate in a double boiler. With the hand-held mixer beat it into the remaining bowl of cream cheese mixture until just combined.
Reduce the oven temperature to 250°F Transfer the milk chocolate mixture to the springform pan, smoothing the top, spoon the white cocolate mixture over it, smoothing the top carefully, and top the white chocolate mixture with the semisweet chocolate mixture, smoothing the semisweet chocolate mixture carefully.
Wrap foil around the bottom and halfway up the side of the pan, put the springform pan in a baking pan, and fill the baking pan with 1/2-inch water.
Bake the cheesecake in the middle of the oven for 2 1/2 to 3 hours, or until the edges are just set. Let the cheesecake cool for 1 hour and chill it, covered overnight. (The cake will continue to set as it cools.) Let the cheesecake come to room temperature.
In a heavy saucepan, heat the cream, milk, and butter over moderately high heat until the mixture just comes to a boil. Add the chocolates gradually, bring the mixture to a boil, stirring occasionally, for 7 minutes. Let the glaze cool.
Pour the glaze over the cheescake, let the cheesecake stand for several minustes, and remove sides of pan.