You can only get the actual cash value (ACV) or fair market value for your vehicle if it is totaled. An insurance company, or if you sue the other party, is only going to pay you the ACV amount and not over it since that will make you whole in the eyes if the law normally.
Asking for more money than the worth of the vehicle is called by courts betterment, since it would put you in a better place than you were by giving you more money than the worth of the car that was totaled. Typically if you car has been totaled out and you do not have means to get a new vehicle due to not being able to get a loan, higher loan amounts, etc than you do not feel that you are whole with just ACV but in the eyes of the law you have been put back in the same place since you have been given the worth of the vehicle you were in at the time of the accident.
If you have negative equity in a car, are upside-down on a loan and thus owe more than it is worth, it is wise to have Gap insurance on the vehicle. Gap insurance would pay the difference between what an insurer pays out for ACV and the loan balance. You still would not be walking away with any money in your pocket to buy a new car but you would have the loan paid off instead of being stuck paying on a loan when you no longer have use of the vehicle due to it being totaled out.
An insurance company will not pay more than the value of a car and the courts will not give you a judgment for more than the value of the car either. It may be blue book value that the insurance company goes by or their own information gathered from local dealers, the NADA guide, etc. If your car has been declared a total loss and you feel that the settlement amount is less than the value of the car than that amount you can negotiate with the insurance company.
To negotiate a higher settlement amount than what you are offered you will need to prove to the insurance adjuster on your claim that your vehicle is worth more than they offered you. You are just trying to prove the fair market value of your vehicle so you can try to get this information from local dealers. Remember you are not going to get more than the actual value of the vehicle but if you feel the insurer's offer is low you can try to show that the vehicle was worth more.