...if I add one more BMS to the same line, one of the communicating BMS will stop communicating (while at the same time) the newly added BMS will communicate successfully.
This does not sound like a physical issue with the bus.
Not sure what you mean with "BMS". But I suggest to read the manual of this device. Has it any limitations in regard to identical devices on one bus ?
My company, for example, works a lot with CANopen devices (sensors). Some older devices had DIP switches for ID selection. limiting the number of devices on the bus (CANopen uses IDs similar to addresses).
You BMS device firmware might be buggy. I would suggest to record the CAN bus traffic in a fail scenario, and evaluate the trace.