I filed an answer to a summary judgment motion, and opposing attorney filed his response

Normally a person files an MSJ, the other person files an opposition and the filing party then files a reply that is to deal with the issues raised in the opposition. If you have facts, evidence, documents or law that deals with the issues raised in the reply, then you can try, although not common to file a response to the reply as long as it is not regurgitation of what is in the opposition. If it is new information and addresses the reply, then the judge may likely review it, if not, raise it in oral argument and offer to sumit any new documents or caselaw at that time, have a copy for the court, yourself and the opposing party.

It is unusual to file anything after a reply (the second filing by the party who filed the motion). However, if the other side introduced new evidence or arguments in the reply, you may be able to file a motion to strike. However, that will depend in part on what court you are in. Different courts have different rules, and you should consider talking to an attorney.

Typical motion practice procedures are: original motion/moving papers; opposition papers; reply papers by movant to address arguments raised in opposition papers. "Sur-Reply" papers are not permitted unless the court has permitted the same. If you feel that the movant has raised an argument, or presented a piece of evidence, that wasn't included in the original motion and is not truly in response to your opposition points ( a movant may not use reply papers to raise new arguments/points), and there is still time before the date the motion is to be argued before the court., you can try writing a letter to the Judge requesting permission to submit Sur-Reply papers, stating the reasons. Be sure to send a copy of the letter to your adversary. In either event, you can make whatever arguements in opposition to the motion you want at the oral arguments to include responding to the contents of the reply papers.