Can a plaintiff file a first amended complaint after the defendants have answered?
Usually yes. Depending on the jurisidiction the plaintiff might need to obtain leave of court before filing it. Not sure what the rule is in Ohio state court since I am not licensed in Ohio. If you are in federal court typically the plaintiff would need leave of court. But in federal court there is usually a deadline provided by which amended pleadings must be filed and as long as the plaintiff moves to amend by that deadline leave is routinely granted.
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Yes, you can file a first amended complaint but you must first move the court for leave to do so. In the motion for leave to file you must explain your reasons for asking to change the original complaint.