UPDATE: It's been a little while since the accident. The car has been deemed a total loss and the other party's insurance company wants to give us $23xx for the car and $18xx if we choose to keep it.

Their offer is less than satisfactory to me. I know that blue book is probably right around there but right now you can't buy another 5th gen accord for that cheap...even one with 200k+ miles on it. So is it possible to challenge their offer and ask for a higher amount and actually expect them to budge? I'm not even sure exactly how much to ask. We've put quite a bit of money into the car and it basically ran perfectly before the accident, at least for a car with 150k miles on the odo.