Yes, its entirely possible, its just contrary to one of the central emulation features of the Amber novels, which is that the Amberites are a great big dysfunctional family: Like any dysfunctional family, they form wierd alliances of convenience and of survival, cabals, and occasionally even all band together when some outside source threatens their chosen status quo, but ultimately the "messed up" ends up being more central than the "love and sharing".
Also, to me at least, its one of the fun features that makes the Amber RPG different than playing, say, high-powered D&D. Its a machiavellian game where your players are not just not expected to be a party, they are expected to often end up being at odds. Playing totally co-operative Amber is a bit like playing totally co-operative Paranoia. It can be done, but it loses a lot of its raison d'etre.
RPGpundit