MySQL Adding New Slave to Master Master Replication Scheme
As long as the values of server-id are different for each server, no planets will be swallowed.  Not even Pluto.

I suggest you turn on binlog and log_slave_updates on all servers.  Then rebuild C from B (as, I assume, you did once).  Then proceed.  I would not want to try to do it from the current C, which is missing stuff.