The Korg volca FM accepts CC's for certain parameters, but the majority of the FM parameters are only adjustable through sysex. Unfortunately it's not as simple as sending a single sysex string for a specific parameter (as the DX7 seems to work) - it only accepts a full sysex for the entire patch.
This means that the full sysex needs to be sent after a parameter is adjusted for the adjustment to take effect in the volca FM (so this is not real-time and causes a slight interruption of audio in the volca). There is an online editor ( https://synthmata.com/volca-fm/ ) that does this and it seems to be configured such that it sends the entire sysex patch immediately after any adjustment is made to any of the parameters.
Can the BCR2000 be configured to do something similar? E.g. assign one button to send a full sysex string containing the current values for all encoders/parameters? Editing the volca FM parameters directly is not bad compared to other FM synths but being able to use the BCR2000, even if non-real-time, would be incredible.