Hi Christina,
The airlines don't usually allow group air in those classes because of the limited availablity of the seats per craft. Group minimum is typically 10 seats and some of these aircraft only have 10-12 depending on the type that they can not afford to have tied up in a group contract.
However, I have very good contacts for this level of air service, particularly with Virgin Atlantic and can secure some excellent rates especially if booked well in advance.