Peel and prepare vegetables.
In a large cooking pot, add water, chicken broth, chicken soup base, black pepper, carrots, potatoes, onions and bring to boil.
Reduce heat and simmer for 15 minutes or until vegetables are tender; stirring occasionally.
Add celery, sweet red pepper and simmer for 5 minutes more. Gradually add mayonnaise to hot soup, whisking until smooth.
Reduce heat to medium and add processed cheese, sharp cheddar cheese and Swiss cheese and simmer for 5 minutes or until cheese melts and soup is creamy; stirring constantly.
Add instant mashed potatoes and stir well.
Let soup sit for 15 minutes before serving.