In the years between its victories in the 1993 European Supercup and the 2001-02 Coppa Italia, the club formerly known as Parma A.C. had the rare distinction of having more European titles than domestic ones (not counting minor domestic titles, like championships of lower divisions or regional tournaments). The tally now stands at 4:4.
Are there currently any clubs that have more European titles than domestic ones (again, excluding minor domestic titles)? I had put my hopes with Nottingham Forest, but it turns out that their tally stands at 3 European titles (2 European Cups, 1 European Supercup) and at least 4 domestic (1 League, 2 FA Cups, 1 Charity Shield), perhaps 8 if you want to count League Cups.