This paper discusses issues relating to the design of a generic, protocol independent communication endsystem to support mobility, heterogeneity, and multihoming. We identify a set of extensions to the communication stack to support various types of mobility. The introduced extensions are based on the concept of communication endpoints, a concept which features in many previous research contributions. We also identify a number of mobile objects requiring mobility support, thus extending the notion of mobility past the mobility of devices to include mobility of content, application services, and human users. We demonstrate our views by comparing session layer mobility management with other solutions, and conclude our analysis with a discussion of design principles for mobility management schemes.