The connected nature of social-ecological systems has never been more apparent than in today's globalized world. The ecosystem service framework and associated ecosystem assessments aim to better inform the science-policy response to sustainability challenges. Such assessments, however, often overlook distant, diffuse and delayed impacts that are critical for global sustainability. Ecosystem-services science must better recognise the off-stage impacts on biodiversity and ecosystem services of place-based ecosystem management, which we term 'ecosystem service burdens'. These are particularly important since they are often negative, and have a potentially significant effect on ecosystem management decisions. Ecosystem-services research can better recognise these off-stage burdens through integration with other analytical approaches, such as life cycle analysis and risk-based approaches that better account for the uncertainties involved. We argue that off-stage ecosystem service burdens should be incorporated in ecosystem assessments such as those led by the Intergovernmental Platform on Biodiversity and Ecosystem Services and the Intergovernmental Panel on Climate Change. Taking better account of these off-stage burdens is essential to achieve a more comprehensive understanding of cross-scale interactions, a prerequisite for any sustainability transition.