I am in a civil lawsuit can I sue for more than the policy limit in nys and if so how do i do it?

From the topic area, it appears that you are talking about a situation where you were injured in a automobile accident. The defendant's policy limits is only important as to how much you can recover from the defendant's insurance carrier. It is not a limitation as to how much you can sue for or recover. In the situation where you would recover damages in an amount above the policy limits, the defendant would be personally liable for any amount above the policy limits.