1. Many animal species show individual differences in behaviour that are partially consistent across repeated measurements. Commonly referred to as personality traits, differences in average behaviours are often correlated across individuals, forming ‘behavioural syndromes’ (e.g. individuals who are more aggressive are also bolder).2. Generally, differences in the average behaviour of individuals explains less than half the variation in behavioural traits. To explain the rest, we need to consider how individuals themselves vary both plastically and unpredictably. 3. Here, we integrate the study of multiple individual differences. With a reproducible worked example based on zebrafish (Danio rerio) behaviours, we give guidance for measuring individual differences in average phenotypes (i.e. personality), responses to an environmental or biological context (i.e. plasticity), and intrinsic variability across time (i.e. predictability, or intra-individual variability).4. Individuality is multi-faceted. By modelling personality, plasticity, and predictability simultaneously, empiricists can quantify how these traits covary across individuals, and test theoretical ideas about phenotypic integration. We provide detailed descriptions and resources for measuring behavioural syndromes, plasticity syndromes, predictability syndromes, personality-plasticity associations, personality-predictability associations, and plasticity-predictability associations. These methods can be extended to incorporate plastic changes in predictability (termed ‘stochastic malleability’). 5. Overall, we showcase the unfulfilled potential of existing statistical tools. Empiricists can use these methods to test more holistic and nuanced questions about the evolution, function, and maintenance of phenotypic variation, for any trait that is repeatedly expressed.