Globally, 2.8 billion people cook with biomass fuels, resulting in devastating health and environmental consequences. Efforts to transition households to cooking with clean fuels are hampered by "fuel stacking", the reliance on multiple fuels and stoves. Consequently, there have been few interventions that have realised the full potential of clean cooking. Here we conduct a structured literature review (N=100) to identify drivers of fuel stacking and specify them according to a psychological model of behaviour, the Capability-Opportunity-Motivation (COM-B) model. We create a taxonomy of stacking and find that the Physical Opportunity domain accounted for 82% of drivers. Our results have important implications for intervention design as they suggest improving opportunity is the most effective pathway to adoption of cleaner fuels. The findings are used to derive recommendations about how policy makers and practitioners can proactively address drivers of stacking in order to foster adoption of clean cooking stoves and fuels.