How many people's taxes can you do with one purchase of turbo tax?

With online TurboTax you get one return per fee.  Each return needs its own account and user ID.

With the CD/download you can e-file up to five federal returns and state returns.   You can prepare more than five if the additional ones are mailed.

https://ttlc.intuit.com/questions/2750704-what-are-the-advantages-of-the-turbotax-cd-download-software-over-the-online-version

Online is only good for 1 return per account.  But you can use the same email address for 5 accounts.   How to start another return in the Online version

https://ttlc.intuit.com/community/using-turbotax/help/how-do-i-start-another-return-in-turbotax-online/00/25596

Or go to the IRS Free File programs

Free File: Do your Federal Taxes for Free | Internal Revenue Service

The Desktop CD/Download program can do unlimited returns and efile 5.

If it's the online version you can only do one persons taxes with turbotax. For any others they need to open their own TurboTax account. For the CD/download version you can do up to 5 different  taxes.