Can I set up one Quickbook username to manage three organizations?

With a single QB (Intuit) username you can add as many company files and in any flavor as your wallet can stand.

Additionally, if you add yourself as an accountant user (with a different email address) you can get a free QBOA accountant special version to more easily manage all of your company files. (plus you can get discounts)

@lotte1 

Yes you may use the same email address as Master Admin to manage those 3 QBO accounts. If you have to open a new QBO account, make sure to click the Buy button to get the discounted price for up to 3 months. If you purchase from the Trial account, you have to pay the regular rate.

https:// quickbooks.grsm.io/US
https:// quickbooks.grsm.io/us-promo