Research: I'm not sure how to find anything for this; I've tried a few spot-searches (etiquette multiple title address and title hierarchy) with no luck, and I've read through the Wikipedia articles on Mr. and Dr..
If a person has multiple professional or social titles, is there any rule of etiquette regarding which comes first?
I'm writing a fanfiction series that's an AU of the show Stargate Atlantis. This AU adds a new profession of "Elementalist", and qualified practitioners are addressed with their element as their title: Fire McKay, Earth Emmagan, Air Sheppard, Water Dex, etc. This title is considered "higher" than most others; the character Rodney McKay has two doctorates, and in an academic or middling-formality environment he would likely be addressed as "Dr. McKay", but the address "Fire McKay" is more formal/respectful. (This being based on the US rather than Europe, he would never be addressed as Dr. Dr. McKay, despite his double doctorate.)
If someone were to address him by both titles, though, which would come first? The related show Stargate: SG-1 has a character (Samantha Carter) who has both a military rank (first Major, later Lt. Col.) and a doctorate, but I'm not sure whether canon establishes an order for her titles (Maj. Dr. Carter or Dr. Maj. Carter, for example) or whether that's dependent on context (military, academic, social, other).
If it makes any difference, McKay is usually treated in non-AU fanfiction (I haven't yet confirmed or denied in canon) as the sort of person who would introduce himself even in social situations as "Dr. Rodney McKay" in defiance of any etiquette regarding self-titling or use of the non-medical title "Doctor" in social settings, but I'm more concerned with how others with more social awareness might address him.
I know that I can make this up, but I'm trying to retain analogues to our world, so if there are any rules, I'd rather know what they are.