CAN I start a second tax filing from the same account that I did my taxes on?

If you're using the TurboTax Online program, you'll need to create a new account for each return. If you're using the TurboTax Desktop program, you can create an unlimited number of returns within the same program but only five can be e-filed. To create a new return in TurboTax Desktop, click on the blue Start a New Return button.

No, not from the same account.  The TurboTax online editions are only for one tax return per account and User ID.

You can use the same email address for up to 5 online accounts.