Spread 1/3 cup Chicken Salad evenly on 1 side of 3 bread slices. Stack Chicken Salad-topped slices; top with 1 bread slice. Repeat procedure with 4 more bread slices and Egg Salad. Repeat procedure with remaining bread slices and pimiento cheese. (You will have 3 stacked sandwiches.)
Beat cream cheeses and milk at medium speed with an electric mixer until smooth. Spread evenly over top and sides of each stack. Cover and chill at least 1 hour or up to 24 hours. Garnish chicken salad sandwich with celery leaves, egg salad sandwich with paprika, and pimiento cheese sandwich with Cheddar cheese, if desired.