Can I sue an insurance company for more than the policy limits?

You would only sue the insurance company in a first party suit. This is a third party suit. The driver himself would be sued and the insurance company defends and indemnifies the driver up to the policy limits, unless there's a bad faith claim$ a bad faith claim generally arises when it is obvious that your son's claims are worth more than the policy limits AND the insurance company does not immediately turn over the policy limits. A person has to be careful not to sign a release when they accept the policy limits because the release will release the driver from a suit. You should consult with a personal injury attorney. As a side note, as a passenger in the vehicle, your son is also covered by the driver's PIP.

The prior answer was very good and covered most of the issues I would discuss. However, it is very important that you make certain that the "policy limits" that are being discussed are the limits for bodily injury per person per accident and the policy limits for medical pay or personal injury protection. If the "policy limits" are for medical pay or personal injury protection, your son would still be entitled to sue the driver under the bodily injury coverage for the amount of that policy limit. Typically, medical payment and personal injury protection limits are used only to pay medical bills and possibly lost earnings or other out of pocket expenses, for example, a nurse or care provider to come into the home. Even though these limits may be exhausted by the medical evac. bill, there may be additional coverage under the bodily limits coverage. Every state has a minimum limits for bodily injury coverage and you can check with your insurance agent and find out how much those limits are in your state. $10,000 seems pretty low and most states have minimum limits above that amount.