Euro-zone banks: How is it possible to have "pan-European" banks that are not too big to fail or impossible to save?

It would be useful to have pan-European banks that operate in many euro-zone countries: this would facilitate the unification of banking practices; it would facilitate bank funding; it would reduce the correlation, country by country, between banks’ situation and countries’ situation. But pan-European banks would be huge, and the question of "too big to fail" and countries’ capacity to save these banks would then arise . A first answer is that the size of banks is calculated in relation to the size of the euro zone and not to their countries of origin, which requires a deposit insurance system in the euro zone and a euro-zone bank recapitalisation fund as a last resort. A second answer is that there would be a need for small or mid-sized pan-European banks, and not only for the largest banks to become pan-European.