Yes you can. In fact, my mom used to change up this recipe for us when we were kids by adding in a cup or two of cheese. She would use shredded cheddar cheese, Monterey jack cheese or mozzarella cheese. Or some good old-fashioned grated Kraft parmesan cheese.u003cbr/u003eu003cbr/u003eIf you want to add some cheese, just stir it in after it is all cooked and mixed together. Give it a few minutes to allow the cheese to melt. OR you could top the American goulash with the cheese and pop it under the broiler for a few minutes to allow the cheese to melt and get bubbly.