Spread cheddar cheese slices with about 2 teaspoons tomato-basil spreadable cheese. Top with provolone cheese slices; spread with about 2 teaspoons garlic-herb spreadable cheese. Top with swiss cheese; spread with scant 2 teaspoons of dill dip. Top each stack with colby-jack cheese.
Cover and chill at least 1 hour. Carefully cut each stack on cracker or place a toothpick in each piece, if desired.