For clarity, what precisely do you mean by "binding" and "bind"
There are two processes for which people use those words and they a completely different things.
One is establishing a connection between the drone and the controller for the purposes of controlling the drone. With the RC-N1/RC231 only one drone can be "linked" (DJI wording) to the drone. If you link a second drone to the controller to linking to the first drone is severed/removed/destroyed.
The other is, as I understand it, the establishment of a connection, for insurance purposes, between the drone and the insured's DJI account and between the drone and the controller. Amongst other things this, I believe, has the ability to ground the drone whilst the wrong DJI account is being used and to ground the drone if the wrong controller is being used.
There is an attempt by someone in the thread
Pair 2 Drones to 1 Remote - How Easy to Switch to get the quirks of this explained but last time I looked I couldn't make sense of the answers but maybe you can.