Can I amend my taxes to add a new W-2 that makes me tax exempt while I work overseas?

Yes, you can. Make sure after you entered the W-2 to put a checkmark by "Worked outside the U.S. - I worked outside the U.S. for an employer that wasn't the U.S. government or its agencies" on the "Do any of these uncommon situations apply to this W-2?" screen. After that go to the foreign income section to answer the questions in TurboTax.

1. Click on the Search box on the top and type “foreign income”.   
2. Click on “Jump to foreign income"
3. TurboTax will walk you through the questions

The IRS will only accept amended returns via mail.

Please see the following information on how to amend your return:

https://ttlc.intuit.com/replies/7276596