Is it possible to add an additional GPU to an Alienware 17 laptop?

no, you cant add RAM to a GFX card.

Additional graphics card RAM is only necessary if your resolution somehow increases. You can't replace the GPU/add another gpu in a laptop though.

WRONG.
Alienware 17 is MXM, which means you can upgrade its dedicated GPU (by replacing it)
I asked dell btw cz i wanted to know too

The actual hard thing is buying a new mobile GPU, but If you give dell a call they might be able to help. Sager and xoticpc replace GPUs if you handle your device to them so that they can replace it (price = fee + GPU)

Agree, and it would be very expensive, especially for a mobile GPU

Mobile GPU's are certainly removable , depending on who made it..... I can't speak for how it stands under Dell ownership but before Alienware was sold to Dell, the units used Clevo Chassis and Clevo certainly allows you to select from among various options upon ordering and assemble.

http/www.lpc-digital.com/sager-np9377-special.html

NVIDIA® GeForce™ GTX 880M 8GB GDDR5 Memory $0.00
Dual NVIDIA® GeForce™ GTX 870M's with 2 x 6GB GDDR5 SLI® Enabled! $50.00
Dual NVIDIA® GeForce™ GTX 880M's with 2 x 8GB GDDR5 SLI® Enabled! $600.00

Click to expand...

http/www.lpc-digital.com/sager-np8298.html
NVIDIA® GeForce™ GTX 860M 4GB GDDR5 Memory $0.00
NVIDIA® GeForce™ GTX 870M 6GB GDDR5 Memory $150.00
NVIDIA® Quadro® K1100M Graphics with 2GB GDDR5 $200.00
NVIDIA® GeForce™ GTX 880M with 8GB GDDR5 Memory! $450.00
NVIDIA® Quadro® K3100M Graphics with 4GB GDDR5! $650.00

When swapping a desktop card, there;'s an easy outlet for the old card via e-bay but selling a notebook card appeals to a extremely small audience. That makes the process quite daunting due to the expense and loss of warranty. The other issue, unlike a desktop, on a notebook it's quite hard to obtain data on the power and cooling systems..... can the power delivery system deliver the required power ? can the cooling system handle the heat ? will the effect on battery life be an issue as the battery in the unit was designed for x hours with the old card.

Add more RAM, I have an M17X R1 and have 8GB installed,

Also an SSD drive will improve performance tenfold.

You can upgrade internal graphics as well, my cards, nvidia 9400m and GeForce GTX280M are mounted on Mxm 3.0B form factor cards, I am looking to upgrade my 9400 when I have the money.