Could I amend a Form 4868 or file a Form 4868 if I did not include my wife?

Hi, I filed a Form 4868 including just my name, but I plan to file a joint return with my wife, so I had to include her name (according to Form 4868's instructions). 

Could I file a second Form 4868 including my wife's name? Please note that I do not owe taxes (the return is to request a refund) and my wife does not have SSN so we will file the Form W-7 to get an ITIN for her. 

Thanks for your help!