You can ask for more after an insurance settlement offer in Chicago, IL, because the first offer marks the beginning of the negotiation process. The initial offer is often low, and insurance companies hope that you will accept it so that they can close the claim quickly at a minimal cost. You have the right to counter a lowball offer by asking for a higher amount. Accepting a settlement too quickly bars you from pursuing additional compensation in the future. That means you will have to cover any additional costs arising from your injury out of pocket. The best practice is to talk to a lawyer before accepting a settlement, especially if you receive the offer immediately after the accident/incident.