I was thinking about the Doctor Who Fiftieth Anniversary Special and how it manages to have a double climax. First, there is an emotional climax that resolves the story with the form-changing aliens which not only brings ten and eleven together but gives the War Doctor his sad determination to go on with his course of action, concluding with the two younger doctors resolving to do this thing that they know is abominable together so that no one of them would have to carry the burden alone. Only after that do we get the action climax which gives another emotional hit.
This got me thinking about other double climaxes, and the one that comes to mind most easily is Raiders of the Lost Ark. Indy has hit what we think is his lowest ebb when he and Marion are locked in the tomb with snakes by Beloq. This is his katabasis, but he rises like all good heroes and engages in a thrilling chase with the Nazis, at the end of which he gets the Ark. The movie could so easily have ended here. But it seems likely that the filmmakers thought they should give the audience more for their money, and so we get an even better climax, indeed the climax to end all climaxes. After all, no earthly climax can beat the wrath of God in terms of grandeur. The final climax, of course, is the Ark ceremony in which the hubris of the Nazis leads to the wrath of God horribly destroying them in a localized but vicious cataclysm.
But I do wonder which order is ideal in terms of multi-climaxes. Obviously, the two have to be different. The difference in Raiders is that the first climax is about what Indy does, demonstrating that he has done all a human can to recover the ark. The second climax humbles both the hero and the villains, showing that they are meddling with forces so much more massive than them that it is genuinely scarier than any number of cobras.
I do not know the answer to my own question of how to arrange double climaxes correctly. However, one of the things I was not all that wild about in The Avengers is that everyone but Tony Stark and Bruce Banner had finished their arcs by the time the actual battle began. The arcs of Widow, Hawkeye, Thor, Maria Hill, Nick Fury, and Cap had all finished, which meant that if you were following them and their struggles then the movie was over for you as soon as the first climax - the battle aboard the Helicarrier - was finished.
Though this does not tell us what we should do, it does constitute a nice little instruction on what not to do. Do not resolve the emotional arcs of your characters before the action climax, because then the action will seem hollow and token. It may well be hollow and token, but you must at least maintain the illusion.