Since its inception Service Science has created a substantial body of knowledge about services and their provision. Most notably, the concept of Service System was defined in order to describe the co-creation of value by the service provider and customer. We introduce the concept of Appreciative System defined by Vickers in the study of the way individuals and organizations apprehend and act on their environment. We show how the appreciative system concept can be applied to a service system model with the SEAM enterprise architecture method.