While a large body of research has focused on the physiological effects of multiple environmental stressors, how behavioural and life‐history plasticity mediate multiple‐stressor effects remains underexplored. Behavioural plasticity can not only drive organism‐level responses to stressors directly but can also mediate physiological responses. Here, we provide a conceptual framework incorporating four fundamental trade‐offs that explicitly link animal behaviour to life‐history‐based pathways for energy allocation, shaping the impact of multiple stressors on fitness. We first address how small‐scale behavioural changes can either mediate or drive conflicts between the effects of multiple stressors and alternative physiological responses. We then discuss how animal behaviour gives rise to three additional understudied and interrelated trade‐offs: balancing the benefits and risks of obtaining the energy needed to cope with stressors, allocation of energy between life‐history traits and stressor responses, and larger‐scale escape from stressors in space or time via large‐scale movement or dormancy. Finally, we outline how these trade‐offs interactively affect fitness and qualitative ecological outcomes resulting from multiple stressors. Our framework suggests that explicitly considering animal behaviour should enrich our mechanistic understanding of stressor effects, help explain extensive context dependence observed in these effects, and highlight promising avenues for future empirical and theoretical research.