In a large mixing bowl, beat butter with an electric mixer 30 seconds. Add sugars, soda and salt. Beat until combined.
Beat in the eggs and vanilla until mixture is smooth. Using the mixer, beat in as much of the flour as you can. Stir in remaining flour by hand. Stir in cherries, nuts, chocolate, and white baking pieces, (Dough will be stiff.)
Drop from rounded tablespoons 2 inches apart on ungreased cookie sheets. Bake in 325 degree F oven 14 to 16 minutes or till golden. Cool a few minutes; remove to a wire rack to cool. Makes 72 cookies.