I'm just a parent, so take this for what it's worth.....In my opinion, a big part of applying for the academies is applying for nominations from your two senators and representative. You have to do that if you're applying to only one academy. You just identify all of the academies you are interested in. Some will ask that you rank them.
The DoDMERB process (medical) and CFA (fitness test) will be faced whether doing one or all.
For each academy, you'll need to do a separate on-line application and write separate essays and get certain teachers to complete some type of questionnaire/recommendation.
It would be good to go ahead and get a thorough resume together. The MOCs will probably request one, and it's helpful when completing all applications for colleges, academies, and scholarships. It's also needed when you go to talk to your ALO, BGO, etc....
I think most of the work would be tied up in writing the separate essays.
Once you have some folks who really like you write some good letters of recommendation, it's not too hard for them to tweak them and recommend you for various opportunities.
I may be forgetting some aspects, but I think I've mentioned the time-consuming ones.