Place pasta shells in inner pot with 8 cups of water (4 cups per box), butter, and salt. Stir. Pressure cook on High for 4 minutes with a quick release. Be mindful of watching in case any foam starts escaping the release.
Strain pasta and return to the pot. Saute on Level 2 for 10 minutes. Add buttermilk, cream cheese, and heavy cream. Stir to combine.
In a separate bowl, combine all remaining cheeses. Add in one handful of cheese at a time and stir until melted. Continue until all cheese is incorporated.