Yes, you can. 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.
Please see the following TurboTax FAQs for more information:
https://ttlc.intuit.com/replies/3300105
And
https://ttlc.intuit.com/replies/3300044
