You have two possible options.
The Internal Revenue Service will begin accepting the 2016 tax year e-file tax returns on Monday, January 23, 2017. If you have already e filed your taxes, you cannot retrieve it from the system ( works like the mailbox).
So after January 23,
1. If your return got rejected for whatever reasons, you can return to the program/account to add your second W-2 along with the corrections needed to be done. You do not need an amendment 1040-X.
2. However, if your return is accepted, you will have to amend your return by filing a Form 1040-X to add your second W-2. You should not try to amend your return until it has been fully processed and you have received your refund or your payment has cleared.
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