To apply for E-2 extension you must submit Form I-129, Petition for Nonimmigrant Worker, along with E Supplement and submit Form I-539, Application to Extend or Change Nonimmigrant Status, for accompanying relatives. Along with it you must submit:
Note: If you file for extension before the expiry of your I-94 you may continue working for 240 days while waiting for the decision. If you file after the expiry of the visa you may stay up to 40 days awaiting the decision. If there is no decision within the 40 days you are supposed to leave terminating your work in the U.S.