Cook pasta as directed on package, adding asparagus and mushrooms for the last 5 minutes of cooking. Drain and return to saucepan.
In small bowl, mix cream cheese, 1/4 cup Parmesan cheese and the milk until smooth. Stir cheese mixture and chicken into pasta mixture.
Cook over medium heat about 2 minutes, stirring gently, until pasta is evenly coated with sauce and mixture is thoroughly heated. Serve with additional Parmesan cheese.