Spread the butter on one side of each bread slice. Heat a large skillet over medium heat. Put 2 bread slices in the skillet, buttered-side down. Layer a slice each of cheddar, Swiss and American cheese on each piece of bread, then cover with another bread slice, buttered-side up.
Cook, pressing the sandwiches occasionally with a spatula, until the cheese melts and the bread is golden, 3 to 4 minutes per side. Repeat to make 2 more sandwiches. Slice each sandwich diagonally in half, then return to the hot pan, cut-side down, to create a crust on the cheese.