Only current year returns can be e-filed. It's possible the IRS could count an amended return as a separate e-file.
See requirement number 5 on page 31 of this IRS Publication: IRS Pub 1345. The IRS requires that software developers ensure there is no more than 5 electronic files from one software package or from one email address.
5. Ensure that it doesn’t accept transmission for more than five electronic returns originating from one software package or from one e-mail address