Errmm..I have 2 laptops that are waaaayyyy crapier than your current system..and I run 5 accounts.
One single core laptop runs 2 instances, and My generic Dell dual-core runs 3 instances. Both laptops only have 2 gigs of ram...and generic video cards.
Granted, I have all my display/video settings turned way down too.

You should be able to get way more out of your Alienware.

Are you using maximizer to set up your screens? Are you setting core affinity?