The Absolute Environmental Sustainability Assessment (AESA) framework is an emerging field in environmental research that aims at comparing the estimated environmental burden generated by a system on its life cycle to the carrying capacity that can be assigned to this system, i.e. the amount of impacts that it can cause without causing unacceptable impairment of ecosystem functional integrity. This paper aims to expand the AESA framework to multifunctional systems. We applied it to a simplified case study based on municipal solid waste (MSW) management, since such a system provides several functions such as reduction of the quantity and toxicity of waste, production of heat, electricity or secondary materials. Thus, we could identify the specific questions that arise from this multifunctionality in the context of AESA.Based on the theory of AESA, we developed a four-steps methodology to identify the most significant impacts at both system and global scales. That methodology consisted of (step 1) quantifying the impacts of the studied system with conventional Life Cycle Assessment (LCA) followed by a normalisation step; (step 2) quantifying the number of beneficiaries from this system; (step 3) identifying impact categories for which the studied system causes significant impacts and global carrying capacities are exceeded; and (step 4) quantifying the Assigned Carrying Capacity (ACC) of the system, based on a utilitarian perspective and its contribution to the satisfaction of human needs.We then applied this methodology to a simplified model of the MSW management implemented in the Lyon Metropolitan Area (France), as a proof of concept. Steps 1 to 3 helped elaborate a hierarchy of impact categories, highlighting which ones should be reduced in priority. Step 4 required significant knowledge about how the functions of the studied system were used, both directly and indirectly, to satisfy human needs. We used national Supply and Use Tables and several simplifying hypotheses to that end. We also tested different sharing principles based on macroeconomic indicators. This variety of sharing principles helped refine the hierarchy developed in Step 3 by identifying which carrying capacities were most certainly exceeded by the studied system.