For the specification and development of large, distributed, and object-oriented systems, it is often advocated that individual components should be developed in an aspectwise manner, where separate descriptions depict various roles or viewpoints of the objects considered. The introduction of such partial specifications requires extra care when reasoning about systems as several specifications of an object may coexist and lead to overlapping information. In this paper, we consider a compositional approach to system development by means of partial specifications of objects. The approach supports stepwise refinement, which enables global reasoning by local refinement steps in an aspect-oriented specification style. For this purpose, a refinement relation is proposed which is suitable for multiple inheritance of behavior and component upgrade.