Set a 6-quart multi-cooker to the saute setting and add the butter. Add the bacon, onions and oregano and cook, stirring frequently, until the onions start to become translucent, 3 to 4 minutes. Add the green chiles, corn and garlic and cook for an additional minute. Add 3 cups of the chicken stock.
In a separate bowl, whisk the cornstarch into the remaining 1/3 cup chicken stock. Add to the multi-cooker and stir well. Cover and position the vent to the sealing setting. Set the multi-cooker to pressure-cook on high for 5 minutes. When the time is up, carefully quick release the steam (it takes about 3 minutes), then remove the lid.
Mix in the heavy cream. Stir in the cheeses until they have melted completely. Check the seasoning; add salt and pepper as needed. Ladle into bowls and serve immediately garnished with the green onions.