"To amend the complaint" means to make changes or corrections to a formal document that outlines the legal claims a person is making in a lawsuit. Full definition
David A. Super, a law professor at Georgetown University, said the lawsuit Ms. Clifford filed on Tuesday centered on a limited contract law matter, but he noted that it also specifically stated that Ms. Clifford would amend her complaint in the future to add the names of people who she said participated in wrongdoing with Mr. Trump and Mr. Cohen. (nytimes.com)
On March 11, 2016, Paramount and CBS filed a First Amended Complaint against Axanar and Peters alleging copyright infringement, contributory copyright infringement and vicarious copyright infringement. (canadianlawyermag.com)