RFID read write module almost works but

I bought the RFID module for arduino (WPI405) and made it work with two types of tag that are used by our client. Great! The client then said “oh and there are two other types of tags we want to use” Hmm. One works; the other does not even register. Indeed the other does not register with the default python variant of the arduino code for the pi from Adafruit. The mystery tags work when scanned with the NFC app I have on a phone, and indeed I cannot see any difference in data between the ones that work and the ones that don’t. I have tried NXP for some advice but they can be slow. Anybody else found a similar problem … and hopefully a solution?