Either side in a case can file a motion. So, if you are the plaintiff or defendant, or the person asking for or responding to a case, you can file a motion asking the court to issue a court order. Motions are filed with the clerk of the court where your case is being heard.
Multiple motions can be filed by each side, but you must have a good reason for filing a motion. You can get in trouble with the judge for filing too many motions or filing motions for the sole purpose of harassing the other side.