No, it is not necessary to submit all 4 W2's for Federal. In TurboTax, you will treat all the pages as if they are 1 W-2 by selecting "Add another line" after entering each state's information. Technically, you do not need to send the IRS a copy of the W-2 unless you are mailing in the return. If you are doing so, you will only need to provide 1 Federal Copy that shows his total wages in Box 1. It does not matter which state is reflected in Box 15.
For your state returns, you will be taxed on all of the income in Missouri as Missouri residents. However, Missouri will give a credit for the amount of tax you pay on that income that you earned in each state to the state in question. In TurboTax, prepare the nonresident states first so that the credit is calculated correctly. Please see this FAQ for more information: https://ttlc.intuit.com/replies/3302052
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