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Biologists often study phenotypic evolution assuming that phenotypes consist of a set of quasi-independent units that have been shaped by selection to accomplish a particular function. In the evolutionary literature, such quasi-independent functional units are called 'evolutionary characters', and a framework based on evolutionary principles has been developed to characterize them. This framework mainly focuses on 'fixed' characters, i.e. those that vary exclusively between individuals. In this paper, we introduce multi-level variation and thereby expand the framework to labile characters, focusing on behaviour as a worked example. We first propose a concept of 'behavioural characters' based on the original evolutionary character concept. We then detail how integration of variation between individuals (cf. 'personality') and within individuals (cf. 'individual plasticity') into the framework gives rise to a whole suite of novel testable predictions about the evolutionary character concept. We further propose a corresponding statistical methodology to test whether observed behaviours should be considered expressions of a hypothesized evolutionary character. We illustrate the application of our framework by characterizing the behavioural character 'aggressiveness' in wild great tits, Parus major.