The Building Information Modelling (BIM) currently contributes to deeply modify the Architecture, Construction and Engineering (AEC) industry by improving data management, task planning, and architecture design etc. Nevertheless, other technologies have also joined this revolution, with the aim of allowing experts to perform better their tasks with them than with only the BIM, particularly mixed reality (MR). However, MR applications can take very diverse forms, because of the multiple design choice possibilities: multiple data sources from the BIM (3D model, worksite monitoring, simulations...), multiple possibilities of visualisations in MR (visual effects, 4D...) and multiple MR interactions (move, write, say, grasp...). Behind MR application design choices, there is a task for which the application has been created. Yet, having BIM-based MR environments that really allow to respond to the original need and that improve task performance is a current difficulty. In this paper, we present our proposal of a methodology for going from BIM to BIM-based mixed reality environments. Our inputs are the AEC tasks which are likely to benefit from being performed in a mixed reality environment, their performance measures (efficiency and effectiveness), and BIM data. Our target is to provide BIM-based mixed reality environments that support specific AEC tasks, and to prove thanks to appropriate indicators that the task performance has improved in MR compared to traditional methods. Thus, we present here the results from our first case studies and their impact on the methodology evolution. Finally, our ongoing and future works are discussed in the last sections.