Unfortunately, your living expenses in another location would not be deductible.
The IRS considers your "tax
home" to be the general area or city where you are employed. If you accepted a job in a city where you or your family do not presently live, then that city is now your tax home. Expenses for living in the area of your tax home are not deductible. You also could not deduct the expenses involved for traveling between your new tax home city and the city of your personal residence.
Here is the example cited in the IRS coverage of this topic:
Generally, your tax home is the entire city or general area where your main place of business or work is located, regardless of where you maintain your family home. For example, you live with your family in Chicago but work in Milwaukee where you stay in a hotel and eat in restaurants. You return to Chicago every weekend. You may not deduct any of your travel, meals, or lodging in Milwaukee because that is your tax home. Your travel on weekends to your family home in Chicago is not for your work, so these expenses are also not deductible. If you regularly work in more than one place, your tax home is the general area where your main place of business or work is located.
Here is a link to the publication which discusses this issue.
What you may want to consider is seeing if this company will hire you as an independent contractor rather than as a W-2 employee. If you were hired as an independent contractor, then you would be considered to be self employed, and your tax home would be the city where your business is located, which would likely be the city where your personal residence is located, as this would be your home office. You could then deduct the cost of traveling to this other city for work as an independent contractor.
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