The least complicated and least expensive way, and the one that puts you at least risk of losing your sanity, is to buy a controlling interest in a company which holds an AOC authorising the operations you want to carry out. A change of control behind the ‘corporate veil’ is not a transfer of the AOC. The AOC continues to be held by the same person. However, CASA will be all over the company when it finds out, to ascertain whether the company continues to have adequate key personnel, financial viability etc.
I occasionally see adverts for AOC’s ‘for sale’, which I assume means someone holds but wants to sell his/her controlling share/s in a company that holds the AOC. (It’s not legally possible for one person to sell an AOC to another person. I suppose a person could sell the piece of paper to another person, just as I could sell my driver’s licence to someone, but it’s useless to the person who paid for it.)