I once worked on a case where the client was hit by a bus operated by the County (so a local government in a particular state), the suit was not entirely barred but there was a cap on damages which would not otherwise exist if say it were a bus being operated by a private company (which would of course generally have a commercial insurance policy as well). It has been almost 10 years but at the time I think the cap was $200,000. Interestingly there is/was a mechanism to request the state (I think the state legislature) waive the damages cap on a case by case basis, but unless your firm was politically connected and donated to political campaigns good luck with that.
So I would imagine that yes, you could.
Strange question, in USA, the is fact you can sue anyone for anything in a civil suit. It's up to a court to decide whether your case has merit or not.