The remedy is to sanction him under the federal court rules and get a standing order restricting his ability to file lawsuits.
In most if not all states, a corporation cannot file a lawsuit if it is not qualified to do business there.
Congress should pass a law providing that neither a person in this country illegally nor any entity owned by persons in this country illegally has standing to file a suit in the federal courts. Alternatively, Congress could provide that the federal courts do not have jurisdiction over any such lawsuit.