Well, support can do anything (or so it seems at times), but requests out of the ordinary will require extraordinary reasons.
In most cases that I konow of, CMDRs who wanted a specific group independent of their commander ID sufficiently bad just coughed up the money for a second account (CMDR pack is currently on sale as part of the Oculus 1 year anniversary...). When that group became sufficiently large (Mobius, Fleetcomm), it got a life of its own (Mobius is two groups now, but CMDR Mobius is still around; Fleetcomm is currently handled by CMDR Grnbrg).