Are the "multiple slots" electrically connected to the Arduino?
OR
Do you just mean places where something can be put and can be identified?
If the latter, how far will they be from the NFC reader?
Do you want to be able to insert several (how many?) cards in different slots at the same time?
This all sounds like an XY problem.
You will get much better advice if you tell us what the project is all about.
...R