Rather than recite a story of an 'over-the-top' request that was fulfilled - which I don't have, mind you since Aman generally left nothing to be desired - I can share with you a small but illustrative anecdote of how Aman took care of me in a very helpful and simple way.
When packing up to leave Amandari, I was happy to see that due to my great packing skills I had managed to fit all of my clothes and belongings into my suitcase with a generous amount of room to spare. I applauded myself on being able to fit everything in much better on this occasion, then when I was originally departing on my trip.
I then called for a porter to pick up my suitcase and then departed the villa on foot, and headed to the reception area to check-out. Upon completing check-out the driver, who was to drive me to Amankila, loaded my suitcase into the trunk of the vehicle, and I noticed him also packing two additional wicker bags that appeared full of stuff. I asked him what that was, and he told me that when he went to pick up my luggage from the villa, he had noticed that I had not packed everything. I had apparently filled two drawers full of clothes that I did not pack into the suitcase! As it turned out, he did not just go to pick up my suitcase and deposit it in the vehicle, he made a thorough check of each drawer and storage space in the villa, in order to ensure that I had not left anything behind, and upon finding my things, he packed them into two complimentary Aman wicker beach bags, and loaded them into the vehicle, all on his own initiative and likely as part of his training. He saved me a huge hassle and I really appreciated it. As a final nice touch, at checkout the staffer put a beautiful Aman mauve leather luggage tag on my suitcase, with my name and address on it.
Anyhow, very absent minded of me. Same thing nearly happened again at Amankila.