ANSWER:
NFC cards and NFC stickers do NOT read AT ALL when stacked precisely on top of each other, and then slowly start working once you introduce more and more misalignment - the more the better


I had some NFC cards and stickers laying around so I decided to stage an experiment to see how NFC tech works when NFC cards are being held close to each other (like it could happen in your wallet) and whether you would be able to continue opening your office doors, etc, without pulling specific NFC card out of your wallet.
- the cards were visually marked from 1 to 5, and the corresponding Plain Text has been written to each card. So each time I would be able to know which specific card has just been read (hint: it is not always the closest card to the reader)
- the Nexus 7 tablet and Nexus 5 phone have been used as readers, together with NFC Tag Writer by NXP mobile app
- the cards and stickers both contained NXP NTAG203 chips - NFC Forum Type 2 Tag 144 bytes user accessible memory
If you want to know the answer right now, here it is:
NFC cards and NFC stickers do NOT read at all when stacked precisely on top of each other. Not in the pack of 5 cards, not even 2 cards. Just do not read, none out of 20 attempts was successful. Same with stickers, even though stickers were cut a bit differently so there was more misalignment with stickers - they still did not read when stacked.
However, if you would introduce some misalignment into 2 cards, it starts reading occasionally - it reads a random tag, not necesserely the one that is close to the reader. The more misalignment you introduce, the better it reads. I will post few more pictures to illustrate "misalignment", but I hope we have our answer now.
HTH, and Happy Scanning!