During the design of complex systems, software architects have to deal with a tangle of abstract artefacts, measures and ideas to discover the most fitting underlying architecture. A common way to structure such complex systems is in terms of their interacting software components, whose composition and connections need to be properly adjusted. Along with the expected functionality, non-functional requirements are key at this stage to guide the many design alternatives to be evaluated by software architects. The appearance of Search Based Software Engineering (SBSE) brings an approach that supports the software engineer along the design process. Evolutionary algorithms can be applied to deal with the abstract and highly combinatorial optimisation problem of architecture discovery from a multiple objective perspective. The definition and resolution of many-objective optimisation problems is currently becoming an emerging challenge in SBSE, where the application of sophisticated techniques within the evolutionary computation field needs to be considered. In this paper, diverse non-functional requirements are selected to guide the evolutionary search, leading to the definition of several optimisation problems with up to 9 metrics concerning the architectural maintainability. An empirical study of the behaviour of 8 multi- and many-objective evolutionary algorithms is presented, where the quality and type of the returned solutions are analysed and discussed from the perspective of both the evolutionary performance and those aspects of interest to the expert. Results show how some many-objective evolutionary algorithms provide useful mechanisms to effectively explore design alternatives on highly dimensional objective spaces.