Combine first 5 ingredients in a mixing bowl; beat at medium speed with an electric mixer 4 minutes. Stir in 1 cup coconut. Divide batter evenly between 2 lightly greased 10-inch round cakepans.
Bake at 350° for 25 minutes or until a wooden pick inserted in center comes out clean. Cool in pans 10 minutes on wire racks; remove from pans, and cool completely on wire racks.
Split cake layers in half horizontally to make 4 layers. Crumble 1 cake layer into fine crumbs. Toss cake crumbs with remaining 1 cup coconut; spread on a baking sheet. Bake at 350° for 10 minutes or until coconut is toasted. Set aside.
Combine sugar and cornstarch. Beat cream cheese at high speed with an electric mixer until creamy; gradually add sugar mixture, mixing well. Add eggs, 1 at a time, beating after each addition. Stir in sour cream and lime juice, blending well.
Place 1 cake layer, cut side up, in the bottom of a lightly greased 10-inch springform pan. Spoon 1/3 cheesecake batter over cake layer; repeat procedure with remaining cake layers and cheesecake batter. (See tip.)
Bake at 325° for 1 hour or until set. Cool completely in pan on a wire rack. Cover and chill at least 4 hours.
Run a knife around the edge of pan, releasing sides. Spread frosting over top and sides of cake. Pat reserved crumb mixture generously around sides and top of cake. Chill at least 1 hour before serving. Store in refrigerator.
Tip: It may be necessary to use a foil collar around the springform pan to hold the cake and cheesecake mixture once it's layered in the springform pan. Cut a piece of aluminum foil long enough to fit around the 10-inch springform pan, allowing 1-inch overlap; starting from 1 long side, fold foil into thirds. Lightly grease 1 side of foil. Wrap foil around outside of pan, greased side against pan, allowing it to extend to 1 1/2 inches above rim to form a collar; secure with string or masking tape. Bake as directed.