The expression of emotion is highly individualistic. However, contemporary speech emotion recognition (SER) systems typically rely on population-level models that adopt a `one-size-fits-all' approach for predicting emotion. Moreover, standard evaluation practices measure performance also on the population level, thus failing to characterise how models work across different speakers. In the present contribution, we present a new method for capitalising on individual differences to adapt an SER model to each new speaker using a minimal set of enrolment utterances. In addition, we present novel evaluation schemes for measuring fairness across different speakers. Our findings show that aggregated evaluation metrics may obfuscate fairness issues on the individual-level, which are uncovered by our evaluation, and that our proposed method can improve performance both in aggregated and disaggregated terms.