Private prosecutions under federal law are allowed under certain federal acts, but they are still rare. Many states have banned private prosecutions by law or through case law, but some states still allow some concept of private prosecution, which actually just means that a person can file a complaint, affidavit or other such document with a magistrate who can then decide whether it should proceed. Even then, a public prosecutor then takes over and can do whatever with the case, including tossing it. So, the simple answer is: Mostly no, not in a meaningful way and only in a few rare instances.