In this article I will argue that text typology based on large corpora and statistical methods may benefit from the notion of the plurality of axes of variation as described in variationist frameworks. In order to investigate these inter-relations, I have focused on the question of which features are specific to one axis of variation, and which features are common to several axes of variation, in a corpus where several dimensions of variation are known. I have performed four independent automatic classifications, corresponding to four axes of variation on a corpus. I use a family of statistical methods, the decision trees, allowing an easy extraction the sets of discriminant morphosyntactic features on each axis. I analyse the intersection between the sets of features. Some features are common to several sets of features and, then, shared between several axes of variation, while other are specific to one axis of variation.