How do I start my second 2023 return in Turbotax desktop?

You can e-file 5 tax returns using the same TurboTax Desktop software. If you use TurboTax Online to file multiple returns, each tax return will need its own Intuit Account with a unique user ID and password. Plus, each tax return will be subject to its own fees.

If you're using desktop version, just click on File, choose New Tax Return (or type Ctrl-N). You probably want to save the one you're currently working on and make sure you give the new file a new name that will indicate what it is.