Select manual on the instant pot for ten minutes. (will take about 6 minutes for the pressure to build up).
Add 1 cup water and 2 chicken breasts and turn on manual/high pressure for 10 minutes. When done quick release.
Open the lid and transfer the chicken breasts to a plate. Use 2 forks to shred.
Preheat oven to 350° degrees and grease a 8 to 9 inch baking dish.
Meanwhile, in a bowl, mix shredded chicken, hot wing sauce, and ranch. Add half quantity of the cheddar and Monterrey jack cheese. Add the cream cheese and stir.
Transfer the mixture into the baking dish and even out the top. Add the remaining 2 cheeses and all of the mozzarella cheese on the top.
Bake uncovered for 35 minutes or until the cheese is brown and bubbly.
Serve with tortilla chips, carrots, celery or crackers.