I am in the middle of a trip that is combining CO, EK and VS business class rewards, with EK on JFK-DXB-MLE-DXB and VS on DXB-LHR-EWR. The EK segments were built by calling and asking many times if certain flights were available and the VS segments by using a combo of checking virgin rewards online as well as calling. Was it a bit of a pain? Certainly, but well worth it in the long run and, well, co.com is not all that helpful in these types of situations.
The VS segment from DXB was booked under VS and the LHR segment under the codeshare.