Depends..

A)  Online Software: IF you e-file, and later have to amend using the Online software, there is no charge to amend unless:
...1)  Unless...The amend change requires one of the higher versions of Turbotax.  Some forms are simply not available in the lower versions. But that mostly applies to amending the Federal part..not state..so you might get away with no charge as long as what you are changing does not also screw up your Federal forms.  Some changes in Federal do not affect it..some do.

...2) Unless.. you do not amend until after mid-October.  Sometimes if you wait too long, you might be required to buy the download software to amend an Online tax return...TTX has some special software downloads for this situation, but they can't always be used.

B)  Desktop Software:  IF you use the desktop software..no extra charge beyond the initial purchase and filing of the originals.  You can amend as long as you have the desktop software installed on your computer..

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Amending:

....i).Amended tax returns can only be printed and mail-filed by you, after you complete the amendment process.

....ii)  you cannot amend, until your originally-accepted tax files have been processed..AND your original refund issued, or you original balance due's have been paid.  The original filing cannot be stopped or aborted.