Airlines based in more than one country
 

Time for another list - Airlines based in more than one country.

So I'll start of with:

SAS - Sweden, Norway, Denmark
LATAM (if you include the whole group) - Chile, Peru, Argentina, Colombia, Ecuador, Brazil, Paraguay

Previously Gulf that used to be based in UAE, Oman, Qatar as well as Bahrain

FR
U2

Many US airlines had at some point in their history larger bases outside of the US. Pan Am for instance had a base in FRA IIRC.

Are we talking focus cities/hubs or legal bases?

For the former, there's a whole load of LCCs that fit the bill (and quite a few in the latter, where they've had to set up legal entities in order to serve a particular country). In Europe, As well as Ryanair and easyJet as above, there's Wizzair, Flybe, Norwegian. Then there's a whole load in Asia-Pac - AirAsia, Air Arabia, Jetstar, Scoot...

There's airlines that serve bases in multiple countries through their subsidiaries (e.g. BA through Sun-Air and Comair). There's KLM Asia, set up to be able to serve the ROC without unduly upsetting the PRC.