The MIDARCH Method is a software design method for exploring software architecture alternatives that use different middleware platforms. First, candidate architectures are modelled based on different architectural styles that are induced by the respective middleware platforms. Candidate styles are chosen using a taxonomy of such styles. The goal is the evaluation of candidate architectures with respect to a goal/question/metric quality model. We illustrate the modelling approach using the Apache Cocoon Web component framework and related technologies, and a taxonomy of their associated styles.