Recent discussions within the mathematical psychology community have focused on how Open Science practices may apply to cognitive modelling. Lee et al. (2019) sketched an initial approach for adapting Open Science practices that have been developed for experimental psychology research to the unique needs of cognitive modelling. While we welcome the general proposal of Lee et al. (2019), we believe a more fine-grained view is necessary to accommodate the adoption of Open Science practices in the diverse areas of cognitive modelling. Firstly, we suggest a categorisation for the diverse types of cognitive modelling, which we argue will allow researchers to more clearly adapt Open Science practices to different types of cognitive modelling. Secondly, we consider the feasibility and usefulness of preregistration and lab notebooks for each of these categories, and address potential objections to preregistration in cognitive modelling. Finally, we separate several cognitive modelling concepts that we believe Lee et al. (2019) conflated, which should allow for greater consistency and transparency in the modelling process. At a general level, we propose a framework that emphasises local consistency in approaches while allowing for global diversity in modelling practices.