Lindström's theorem, are there any other maximal elements?

Question

Lindström's theorem says that first order logic is the strongest logic that follows compactness and Löwenheim–Skolem. By strongest it means it is a maximal element under the ordering of A$\leq$B when B can model anything A can. So there could be some other logic that is also maximal, is any such logic known, or is it suspected that none exist?