Running cross browser tests using different user logins.

You can use parameters and not only pass in the browser name but the login information.  I suggest reading those from a data file (.csv or Excel) rather than putting them in variables like the examples here.  That way you can update your data outside TC if the login information changes.

https://support.smartbear.com/testcomplete/docs/app-testing/web/general/cross-browser/parameterizing.html