Where's the button to start a new return (for family member)?

The TurboTax online editions are only for one tax return per account and User ID.  If you want to start another tax return using the online editions you will need to create a new account with a new User ID.

Online is only good for 1 return per account.  But you can use the same email address for 5 accounts.  You can start another return in TurboTax Online by:

1. Logging out if you are in your account
2. Choose what TurboTax Online product you want to use for the second return
3. Create your account screen
4. Set up a new login for the second return
5. Start working on the new return

The Desktop program can do unlimited returns and efile 5.  You can buy the Desktop CD/Download program directly from Turbo Tax

TurboTax® 2021-2022 CD/Download Tax Software, Compare Desktop Tax Preparation

Or buy Turbo Tax at several stores like Costco, Sam’s, etc.   Where can I buy Turbo Tax Desktop program?

https://ttlc.intuit.com/community/choosing-a-product/help/where-can-i-buy-the-turbotax-software/00/25893