1040X is a replacement return.
You can prepare a 1040X with new W-2 and include a copy of the earlier (defective) return and earlier (defective) W-2. It would be optional to highlight the replacement W-2 or by cover letter stating what is enclosed.
If you include payment and prove the date of submission before April 15, you would hopefully get ahead of the machinery that might try to provide some deficiency calculation.
Paying for the error is up to your employer. This is difficult as time spent might be a few changes to your forms, reprinting and re-filing for some people. Others may have extensive other holdings and a re-do on their tax filings might cost over $1000. (very uneven effect among employees)
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Curt Harrington Patent & Tax Law Attorney Certified Tax Specialist by the California Board of Legal Specialization PATENTAX.COM This communication is general information and not legal advice, and does not create an attorney-client relationship. This communication should not be relied upon as any type of legal advice. Please note that no attorney-client relationship exists between the sender and the recipient of this message in the absence of either (1) a signed fee contract and (2) remission of an agreed-upon retainer. Absent such an agreement and retainer, I am not engaged by you as an attorney, nor is any other member of my law firm.
You might politely request your employer pay the cost of amending your return. Unfortunately, the new W-2 should follow the W-4 you submitted to determine the level of withholding, and you are ultimately responsible for additional tax due (if any). Moreover, it does not seem that there would be any additional penalties or interest that you would not already be responsible for (i.e., if you under-witheld). If you need someone to take a look at your return, I am in you area. I can be reached at (425) 451-9572.