It may be possible, depending on a number of factors, the most fundamental of which is arguably the nature and truth/falsity of the statements.
This answer is provided for informational purposes only, does not create an attorney-client relationship, and is not to be relied upon as legal advice or applied to specific situations. Legal advice is provided only upon execution of a written retainer agreement and after a comprehensive consultation in which all relevant facts are discussed and reviewed.
What you want is known as an Injunction. However, getting an injunction against speech is no simple matter. You will need to conduct a full trial, demonstrating the falsity of the statements and that they cause you harm.
If you want a Preliminary Injunction, that is almost impossible to get in a defamation case. Bantam Books, Inc. v. Sullivan, 372 U.S. 58 (1963); Erwin Chemerinsky, Constitutional Law: Principles and Policies 918 (2002) (“The clearest definition of prior restraint is an administrative system or a judicial order that prevents speech from occurring”). The term “prior restraint” is used “to describe administrative and judicial orders forbidding certain communications when issued in advance of the time that such communications are to occur.” Alexander v. U.S., 113 S. Ct. 2766, 2771 (1993). The essence of a prior restraint is that is places specific communications under the personal censorship of a judge. Bernard v. Gulf Oil Co., 619 F.2d 459, 468 (5th Cir. 1980).
You should start with a demand letter from a retained attorney to this "antagonist" if you have his/her name, advising him/her that a refusal to take the false claims down by a specific deadline will result in a defamation action being filed. That may achieve your goal; otherwise you will need to file a defamation lawsuit and seek to obtain a court order forcing the party and the websites where the posts currently exist to remove the same. If the defendant chooses to defend his or her statements, then you may get into a free speech debate, but often in cases such as this the defendants simply default and a default judgment is issued, or else they immediately settle and withdraw the posts. It depends on your particular factual circumstances. The most problematic issue is if you lack the name of the "antagonist" -- because then you do not know who to go after to take the postings down. You will then need to determine who this person is from the websites that have permitted the postings.
I hope that provided some help. Good luck.
The information that is placed in this response is for informational purposes only and does not create an attorney-client relationship with Thomas P. Howard, Esq., nor is it intended to be relied upon as a replacement for legal advice from an attorney.