The symmetric shock of the Covid-19 pandemic has come with heterogeneous consequences across the world. Within the common institutional framework of the European Union, the outbreak has put under extreme stress governance and interplay between the national and supranational level. Under some coordination, responses have remained largely in the hands and on the shoulders of the Member States. In this context, the article classifies pandemic outbreaks and responses along the containment and fiscal support dimensions to uncover whether a common model for Covid-19 crisis management arises across the EU27 or rather different policy choices patterns emerge within the continent. Based on indicators covering the three dimensions derived from the Oxford Covid Government response tracker, the John Hopkins CSSE Covid-19 database and the European Commission Autumn Forecasts, the paper employs hierarchical cluster analysis to uncover response group across countries and characterize them by the outbreak, containment and fiscal support strengths, delineating as well the geographical distribution across and within the clusters. The findings present the heterogeneity of response models, robust to alternative specifications and timeframes across the first and the second wave, deriving broader implications for the outlook for the vaccine-roll out and exit from the crisis. The dynamics in 2020 are also considered in the context of the shortcomings of supranational governance within the EU and the current policy reform debate, highlighting the high stakes for the upcoming Conference on the Future of Europe. The contribution of the work is furthered by offering a systematic methodology and framework to study heterogeneities of pandemic responses within the EU paving the way for further analysis of contributing factors explaining decision-makers policy choices as well as performance concerning political, social and economic outcomes across the models.