Even if it were possible, the real killer here is that a more powerful graphics card would require More power! This extra power might not be available, or it could reduce the time that the laptop could be powered by the battery alone, or it could increase the heat that the laptop generates beyond a point that the laptop could sustain.
Nope. Pretty much impossible to replace anything but the ram in a laptop. Sorry.
You do know that most Alienware laptops have removable mPCI video cards right, and your statement, although may apply to 95% of the laptops out there that have soldered on BGA style graphics chips, systems like Alienware are the exception and therefore your statement is wrong and if you don't know the answer for sure, don't make such a statement.
Alienware laptops generally allow you to upgrade the graphics card.
The Alienware M15x has an expandable slot for the graphic card. It is MXM 3.0b. However, the actual dimensions might be proprietary meaning it will only accept a MXM graphics card that has been designed specifically for the M15x.
Below is a link to eBay for a Radeon HD 6970 card that is strictly for the M15x. You should call the seller and confirm that it will work with your version of the M15x. There are at least 3 revisions of that laptop and I think your's is revision 2 or "M15x R2". It sells for $450 + shipping.
MXM format graphic cards are not sold in retail, therefore, the only real choice is to buy it through ebay. You can try to contact Dell and ask if you can buy a MXM graphics card through them. But I doubt they will.