UPDATED FOR TAX YEAR 2019
If you used TurboTaxOnline for your return, you will have to open another account for your parents' return/extension. Your TurboTax login is connected to one return,but you can have 5 accounts under your e-mail address.
To start a new return in TurboTax Online, please follow the directions in this TurboTax Help article:
How do I start another return in TurboTax Online?
[Edited | 3/31/2020 | 8:40am PDT]