In a medium mixing bowl, combine the cream cheese, sour cream, mayonnaise, ketchup, and mustard together until smooth.
Mix in the corned beef, sauerkraut, relish, and some of the cheese.
Spread the mixture into a baking dish and top with remaining Swiss cheese.
Bake until warm, bubbly, and the cheese is browned.
Sprinkle parsley over the dip if desired and serve with rye chips, triscuits, or toasted rye bread.