Preheat oven to 350˚F. Line cupcake pans with paper liners.
Combine flour, sugar, baking powder, salt, shortening, milk and vanilla in a large mixing bowl. Mix at low speed for 2 minutes. Scrape bowl. Add egg whites and additional whites or yolks, and mix at high speed until fluffy and smooth, approximately 2 minutes.
Fill liners 1/2 to 2/3 full of batter. Do not overfill. Bake 20-25 minutes or until toothpick inserted in center comes out clean. Let cool 10 minutes in pans then remove from pan, and place on wire racks to cool completely.
In a piping bag, wipe the blue frosting against the side of 1/3 of the inside of the bag. Next wipe the green next to it, spreading it in the same fashion. Fill in the rest of the bag with the yellow frosting.
Close up the piping bag and pipe out a little frosting until the three colors start to come together. Pipe the rest of the frosting on to your cupcakes.