This study examines the dynamics of sustainability transitions in the EU-27 during the period 2015-2024, focusing on the role of different stakeholders and the emergence of distinct convergence patterns in sustainability performance. The theoretical framework integrates sustainability transition theory, stakeholder governance, and the literature on convergence and club convergence, interpreted through the socio-technical multi-level perspective and the concept of institutional lock-in. A test model is developed based on four stakeholder-specific indices: the Government Sustainability Index (GSI), Environmental Sustainability Index (ESI), Population Sustainability Index (PSI), and Business Sustainability Index (BSI), complemented by a Composite Sustainability Index (CSI). The indices are constructed using min–max normalization of harmonized data from Eurostat, the European Environment Agency, and the Sustainable Development Report. The empirical analysis combines K-means clustering, compound annual growth rate (CAGR) calculations, and correlation analysis, complemented by a robustness module testing alternative weighting schemes, z-score normalization, and ±10% variations in index components. The results reveal four relatively stable sustainability tiers among EU member states, an S-curve-type relationship between initial sustainability tiers and subsequent growth, and a consistent hierarchy in stakeholder response speeds (ESI > GSI > PSI). A clear structural slowdown after 2019 is also observed. The main findings remain robust across alternative methodological specifications. The study contributes to the quantitative integration of the multi-level perspective on sustainability transitions into a stakeholder-based composite index framework for cross-country analysis within the European Union.