Everything is open to negotiation, but it is pretty unlikely they will budge.
Consider that you've already gone through the negotiation phase (whether you negotiated or not), both sides accepted the terms and they're formalized the offer.
If you go back now, how do you think they would feel? Let's flip it around. Suppose they already sent you the offer letter, then a day later they sent you another one, with worse terms (for you). How would that feel? Would you still consider the job, or would you think they must think I'm a sucker and are trying to play me to see how much they can get?
One thing to note: if you let your original job know you were looking, or you have an offer, you're dead: you can kiss your future at the original job goodbye. You will be moved to the top of the 'layoff' list and the bottom of the 'raises and promotions' list.
Also—unlikely, but I've seen it happen—if original company finds out who offered you the position, they can torpedo your new gig with a few well-placed phone calls. Best advice in this area is to keep quiet about the new job until after you start, if you intend upon taking that job.