In VERY simple terms...
The Authority would allocate you an FOI (Flight Operations Inspector).
He/she would thoroughly look at your initial set up plans, including your full set of Operations Manuals, interview your Form 4 AOC post holders who normally should already be in your full time employ and make a decision based on what they discover, there is a hell of a lot more digging that they do, but I am keeping it simple.
Engineering wise a similar appointment would be made and a similar process follows.
The above process could take anything up to a year (someone correct me if I am wildly wrong)
If both were satisfied then the CAA Financial guys get involved and before any AOC is granted they must be able to see that you have the money in the bank, or the backing to keep your commitments (getting harder these days)
To put another aircraft on your AOC exactly the same process must occour, and again can take a long time for them to be satisfied, if you were swapping from Cargo to Pax it can take a VERY long time for any sort of approval to be given, even if it is the same aircraft type.
My advice (for what its worth) is dont try to pull the wool over the Authority's eyes, they have seen it time and time again and will probably see straight through it, tell them your plans, work with them and they will be much more helpful if you tell the truth, otherwise they will just say no, and unlikely to give you much time of day in the future.