The TurboTax Deluxe and higher online versions, require you to purchase each state you need, no matter which version you choose. Only if you are using the desktop version, then the 1 state is already included with Deluxe or higher versions and then you purchase each additional state.
You can prepare and paper file as many states as you want in the desktop version, but you can only e-file up to 3 different states per each federal return with desktop. The Online version will allow you to prepare and e-file up to 5 state returns per federal tax return. So if e-filing multiple states is most important to you, consider TurboTax Online.
NOTE: When you are preparing returns for multiple states, you'd need to do your non-resident states first and then your resident state. You might not even have to file a state return at all if you live and work in a state that doesn't collect income tax. See here for those states: https://ttlc.intuit.com/questions/1901267-which-states-don-t-have-income-tax
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