No. There is no way to indicate more than one other state on Form IT-2 and the form instructions state that you do not have to.
Under Multiple W-2 Records for one federal Form W-2, Form IT-2 says “Do not fill in additional W-2 Records to report withholding by more than one other state for the same wages.”
New York is only interested in New York wages and withholding. If you are filing multiple non-resident state returns and claiming a credit against NY tax, you will have to include copies of the other state returns (which TurboTax will do) in order to get credit for tax paid to the other states.
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