Design of stable software architectures has increasingly been a deep challenge to software developers due to the high volatility of their concerns and respective design decisions. Architecture stability is the ability of the high-level design units to sustain their modularity properties and not succumb to modifications. Architectural aspects are new modularity units aimed at improving design stability through the modularization of otherwise crosscutting concerns. However, there is no empirical knowledge about the positive and negative influences of aspectual decompositions on architecture stability. This paper presents an exploratory analysis of the influence exerted by aspect-oriented composition mechanisms in the stability of architectural modules addressing typical crosscutting concerns, such as error handling and security. Our investigation encompassed a comparative analysis of aspectual and non-aspectual decompositions based on different architectural styles applied to an evolving multi-agent software architecture. In particular, we assessed various facets of components' and compositions' stability through such alternative designs of the same multi-agent system using conventional quantitative indicators. We have also investigated the key characteristics of aspectual decompositions that led to (in)stabilities being observed in the target architectural options. The evaluation focused upon a number of architecturally-relevant changes that are typically performed through real-life maintenance tasks.