Depending on how long you've had it and where you bought it you may be able to trade it for a unit with 8 GB RAM for only the difference in cost, essentially a return and new purchase transaction. Additionally from stories I have heard here Microsoft has been surprisingly generous in these situations. YMMV.
However if you were thinking adding RAM would be cheaper on the aftermarket that's not possible. There are no slots, RAM is soldered on the motherboard. under the category of is it possible: It would be an extraordinary technical feat as you would have to expertly disassemble the device then remove the existing RAM and replace it on the motherboard then reassemble the unit. Level of difficulty is 12 on a scale of 1-10 and would be more expensive than buying a unit with 8 GB RAM.
That said if the Surface line becomes very popular I wouldn't be surprised to see a "Mikegyver" type outfit, offering 16GB RAM upgrades for $800- $1200. Totally not worth the price but highly profitable.