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 vanilla; beat until blended.
Combine flour and baking soda; add to butter mixture alternately with buttermilk, beginning and ending with flour mixture. Beat at low speed just until blended after each addition. Stir in coconut and pecans.
Beat egg whites at high speed until stiff peaks form, and fold into batter. Place 36 paper baking cups in 3 (12-cup) muffin pans; spoon batter into cups, filling half full.
Bake at 350° for 18 to 20 minutes or until a wooden pick inserted in centers comes out clean. Remove from pans to wire racks, and let cool completely (about 45 minutes).