TurboTax Basic, Deluxe, Premier, and Home & Business software lets you prepare and paper-file as many state returns as you want.
However, you can only e-file returns in up to three different states for each federal return you prepare. The rest will need to be paper-filed.
If e-filing multiple states is important to you, consider TurboTax Online; it lets you e-file and/or paper file up to five state returns per federal return.
Tip: When preparing returns in multiple states, it's best to do your nonresident and/or part-year resident state returns first, and your resident state last.