Yes, in a personal injury lawsuit you can sue for more than the insurance coverage or insurance limits of the defendant’s insurance policy.
If you get a judgement for more money than the insurance limits of the person you are suing you may be able to collect the excess of the judgement. You can go against the defendant personally. If your personal injury lawsuit is as a result of an auto accident, you can also claim under-insurance coverage from your own insurance policy.
Almost everyone’s car insurance policy will have under-insurance coverage. This means, if the person you are suing has less insurance coverage than you do, you can sue your own insurance company to cover you for the difference between the defendant’s policy and your own.
For example: if you got a judgement in a motor vehicle accident claim for $500,000 and the defendant’s insurance limits are only $200,000 while your limits are $1,000,000. You will collect $200,000 from the defendant’s insurance company and the excess, $300,000, from your own insurance company pursuant to your under-insurance coverage.