Character Analysis
While this band of concierges functions symbolically in the film, they're also characters in their own right, so let's remind ourselves who they are.
We have M. Ivan of the Excelsior Palace (played by the ubiquitous—in Anderson films and in life—Bill Murray), Monsieur Georges of the Chateau Luxe, Monsieur Dino of the Palazzo Principessa, Monsieur Robin of l'Hotel Cote du Cap, and Monsieur Martin of the Ritz Imperial.
Individually, they don't get much screen time, but collectively we see from them what it means to be a concierge. Each of these characters is controlling (we see them conducting birthday parties and making sure the soup tastes perfect), accommodating (they give polite directions and CPR), has a lobby boy underling which they, not unkindly, boss around, ("take over" becomes the trope of this montage), and, most importantly, are loyal to one another.
Each of the Society of the Crossed Keys members is in the middle of an act of varying importance, yet each immediately drops what they are doing to respond to the call of another concierge.