Using a novel cross-European dataset on bank internationalization, the paper accounts for organizational and geographic complexity and evaluates its impact on systemic risk and how both the 2008–09 global financial crisis and the 2010–11 European sovereign debt crisis might have modified such an impact. Ahead of the crisis (2005–07), results suggest that bank complexity materially reduces systemic risk and enhances stability, as it encourages banks to take on more diversified risks. While such a relation is inverted during the crisis (2008–11) and after the crisis (2012–13), consistent with the view that, during distress times, international banks have less ability to monitor cross-border risks. Further evidence show that, regardless of the period, the effect of complexity on systemic risk is accentuated for ‘too-big-too-fail’ banks and banks with strong activity diversity. Conversely, complex banks with merger-acquisition history and banks operating networks of foreign branches mitigate systemic risk during the acute crisis and the later stage of the crisis, respectively. The results are robust to the use of alternative measures of systemic risk and complexity, and numerous additional tests. Findings bear critical policy implications for financial regulations.