The problem of formalizing architectural styles has been recently tackled with the introduction of the concept of architectural type. The internal behavior of the system components can vary from instance to instance of an architectural type in a controlled way, which preserves the absence of deadlock related architectural mismatches proved via the architectural compatibility and interoperability checks. In this paper we extend the notion of architectural type by permitting a controlled variability of the component topology as well. This is achieved by declaring some component connections to be extensible, in the sense that the number of connected components can vary from instance to instance of an architectural type. We show that such a controlled variability of the topology is still manageable from the analysis viewpoint, as the architectural compatibility and interoperability checks scale with respect to the number of components attached to the extensible connections.