Beat butter and shortening at medium speed with an electric mixer until fluffy; gradually add sugar, beating well.
Add egg yolks, 1 at a time, beating until blended after each addition. Add extracts; beat just until blended. Set mixture aside.
Combine buttermilk and sour cream, stirring until blended. Combine flour, baking soda, and salt, and add to butter mixture alternately with buttermilk mixture, beginning and ending with flour mixture. Beat at low speed with an electric mixer until blended after each addition.
Beat egg whites until stiff peaks form; fold into batter. Fold in coconut, pecans, and cherries. Pour batter into 3 greased and floured 9-inch round cakepans.
Bake at 350° for 20 minutes or until a wooden pick inserted in center comes out clean. Cool in pans on wire racks 10 minutes; remove from pans, and cool completely on wire racks.
Spread Cherry-Nut Cream Cheese Frosting between layers and on top and sides of cake. Store cake in refrigerator.