The use of a compact set of climate change indexes enhances our understanding of the combined impacts of extreme climatic conditions. In this study, we developed the modified Climate Extremes Index (mCEI) to obtain unified information about different types of extremes. For this purpose, we calculated 10 different climate change indexes considering the temperature extremes, extreme precipitation, and moisture surplus and drought over the Europe-Mediterranean (EURO-MED) region for the 1979-2016 period. As a holistic approach, mCEI provides spatiotemporal information, and the high-resolution grid-based data allow us to accomplish detailed country-based and city-based analyses. The analyses indicate that warm temperature extremes rise significantly over the EURO-MED region at a rate of 1.9% decade(-1), whereas the cold temperature extremes decrease. Extreme drought has a significant increasing trend of 3.8% decade(-1). Although there are regional differences, extreme precipitation indexes have a significant increasing tendency. According to the mCEI, the major hotspots for the combined extremes are the Mediterranean coasts, the Balkan countries, Eastern Europe, Iceland, western Russia, western Turkey, and western Iraq. The decadal changes of mCEI for these regions are in the range of 3-5% decade(-1). The city-scale analysis based on urbanized locations reveals that Fes (Morocco), Izmir (Turkey), Marseille and Aix-en-Provence (France), and Tel Aviv (Israel) have the highest increasing trend of mCEI, which is greater than 3.5% decade(-1).