Separate eggs. Allow egg yolks, egg whites and butter and to stand at room temperature for 30 minutes. Meanwhile, grease and flour three 9" x1 1/2" round baking pans; set pans aside. In a medium bowl, stir together flour, baking soda and salt; set aside.
In a large mixing bowl, beat butter and shortening with an electric mixer on medium to high speed for 30 seconds. Gradually add sugar, about 1/4 cup at a time, beating on medium speed until light and fluffy (4 to 5 minutes), scraping sides of bowl occasionally. Add egg yolks, one at a time, beating well after each addition. Beat in vanilla.
Alternately add the flour mixture and buttermilk, beating on low speed after each addition just until combined. Stir in the 1 2/3 cups coconut and 1/2 cup chopped pecans.
Thoroughly wash beaters. In a medium mixing bowl, beat egg whites on medium to high speed until stiff peaks form (tips stand straight). Gently fold about one-third of the stiffly beaten egg whites into cake batter to lighten it. Fold in remaining egg whites. Pour batter evenly into the prepared pans, spreading evenly.
Bake in a preheated 350 degree oven for 22 to 28 minutes or until a wooden toothpick inserted in centers comes out clean. Cool layers in pans on wire racks for 10 minutes. Remove layers from pans; cool thoroughly on wire racks.
To assemble, place the first cake layer, bottom side up, on a serving plate. Using a flat-bladed spatula, spread about 3/4 cup of the Cream Cheese Frosting over the first cake layer. Sprinkle with 1/2 cup of the coconut and 1/4 cup of the pecans.
Add second cake layer, bottom side down. Spread with additional 3/4 cup frosting. Sprinkle with the remaining 1/2 cup of the coconut and the remaining 1/4 cup of the pecans.
Add third cake layer, bottom side up. Add a thin coating of frosting to entire cake to seal crumbs, preventing them from mixing with frosting. Beginning with the sides and finishing with the top, evenly spread remaining frosting over cake, swirling and sculpting as you go. Garnish top and sides of cake with additional coconut and chopped pecans.
To Make The Cream Cheese Frosting: Cut cream cheese into small pieces (do not soften). In a large mixing bowl, beat the chilled cream cheese pieces, the butter, vanilla and salt with an electric mixer on medium speed until smooth.
Gradually add powdered sugar, about 1/2 cup at a time, beating well after each addition. If needed, gradually add 1 to 2 tablespoons milk to reach spreading consistency.