Is it possible to create a new GATT service/characteristic at runtime on a peripheral device from a central device? When a peripheral device comes near a central, I am trying to store an id onto the peripheral device so that I can recognize the device later when it connects to a different central.

I have tried connecting/pairing with the peripheral devices and I am able to read/write GATT characteristics that are already defined on the device. Is it possible to do the same for ones that are not defined on the peripheral?

As I can understand, these services/characteristics have to be defined by the peripheral (GATT server) so that any GATT client can access them, so what I am trying to achieve may not be possible.