Make-ahead tip: Freeze each baked layer up to 1 month. Unwrap and thaw at room temperature 2 hours.
Beat shortening and butter at medium speed with an electric mixer until creamy; gradually add sugar, beating until blended. Add egg yolks, 1 at a time, beating just until blended.
Combine flour, baking powder, and salt; add to butter mixture alternately with milk, beginning and ending with flour mixture. Beat at low speed until blended after each addition. Stir in vanilla and almond extracts.
Beat egg whites at high speed with electric mixer until stiff peaks form. Fold into cake batter. Spoon batter into 1 greased and floured 13-inch oval cakepan.
Bake at 350° for 35 to 40 minutes or until a wooden pick inserted in center comes out clean. Cool in pan on wire rack 10 minutes; remove from pan, and cool completely on rack.
Note: Repeat procedure for baking the second 13-inch layer. Prepare cake batter 4 1/2 more times. Spoon 10 1/2 cups batter into a greased and floured 16-inch oval cakepan. Bake at 350° for 40 to 45 minutes. Spoon 5 1/4 cups batter into 1 greased and floured 10-inch oval cakepan. Bake at 350° for 35 to 40 minutes. Repeat procedure with remaining batter for baking the second 16-inch layer and the second 10-inch layer.