The integration of sustainability principles into the assessment of companies along the supply chains is a growing research area. However, there is an absence of a generally accepted method to evaluate corporate sustainability performance (CSP), and the models and frameworks proposed by the literature present various important challenges to be addressed. A systematic literature review on the supply chain at the corporate level has been conducted, analyzing the main strengths and gaps in the sustainability assessment literature. Therefore, this paper aims to contribute to the development of this field by proposing an assessment framework a leading company can adopt to expand sustainability principles to the rest of the members of the supply chain. This proposal is based on best practices and integrates and shares efforts with key initiatives (for instance, the Organizational Environmental Footprint from the European Commission and United Nations Environment Programme and the Society of Environmental Toxicology and Chemistry UNEP/SETAC); moreover, it overcomes important limitations of the current sustainability tools in a supply chain context consistent with the circular economy, the Sustainable Development Goals (SDGs), planetary boundaries, and social foundation requirements. The results obtained create, on the one hand, new opportunities for academics; and, on the other hand, in further research, the use of this framework could be a means of actively engaging companies in their supply chains and of achieving the implementation of practical and comprehensive CSP assessment.