The TurboTax online edition are only for completing one tax return per account and user ID. To start another tax return using the online editions you would need to create a new account with a new unique user ID. State returns are an additional charge.
TurboTax online editions - https://turbotax.intuit.com/personal-taxes/online/
If you need to file multiple tax returns, it is more cost effective to use the TurboTax desktop editions where you can create as many tax returns as needed without any further charges. One State software download is included in the purchase price (Except for Basic)
TurboTax desktop editions - https://turbotax.intuit.com/personal-taxes/cd-download/