The graphics card in the laptop is 1GB GDDR5 Radeon HD 6770M Graphics. I've checked AMD's site and it looks like this particular card will support up to 6 independent(different) displays. I'm not sure if this is really feasible but it would be nice.
I would like to have the ability to run 3 or ideally 4 different displays on different monitors (with the laptop screen) being one of them and I'm not sure if this is doable and what specifically I need to be aware of beyond the graphics card ability to support this.
Looking at the specs of your selected laptop, it appears to only have one VGA and one HDMI graphic output. You may or may not be able to use both at the same time. My recommendation would be to use a Matrox TripleHead2Go to have four monitors (Laptop +3 monitors).