An EU Head of State, eh? Empires are not appropriately capped by republican institutions, but by monarchies.
So, how about a monarch dynastically connected to almost every other Royal House still reigning in the EU (I can’t find a link to Luxembourg, but perhaps I just need to look harder), who has plenty of German blood, and whose Heir Apparent’s father has practically nothing else, although he is closely connected (as the monarch herself is also, if more distantly, connected) to the House that, until less than a century ago, reigned over Estonia, Latvia, Lithuania, and much of present-day Poland? And how about a monarchy effecting bonds of peace with 15 other sovereign states, plus their Associated States and their Dependencies, in the Americas and the Pacific, something that no other monarchy can offer?
In other words, might the last Emperor of India’s daughter be the first Empress of Europe?