Yes. In most negligence claims, victims are entitled to recover compensatory damages that include all economic and noneconomic losses, but the insurance company must only pay compensation up to the policy limit. However, if the at-fault driver was driving under the influence, the victim may be entitled to much more compensation in the form of punitive damages.
Juries award punitive damages in cases where the at-fault driver exhibited “willful misconduct, fraud, wantonness, malice, or that entire want of care which would raise the presumption of a conscious indifference to consequences.” O.C.G.A. § 51-12-5.1(b). Under Georgia law, DUI meets this standard. If you can prove that the accident was caused by drunk driving, there is no cap on the amount of punitive damages you can receive—it is up to the jury to decide.