No, not with two different browser-tabs. The security is in the session-cookies.
But you have other options to be logged in with two different users at the same time:

- while already logged in via a normal tab, open a private-tab (Ctrl-Shift-p) and log in with another user;

- open another type of browser, FF, IE, Opera, Chrome and log in with another user;

Hm, I now see Wouter beat me to it. Should not have gotten coffee first.

Why would you want to be able to log in with two users? I think there is no practical application for actual users here, correct?

The idea of Mendix is that it is a single page application – one session is linked to one user within a single app. To allow for this, a cookie is stored. Every time you re-open the page, that cookie will be found and you will be automatically logged back in. 

That being said, you can start a private browser tab using the shortcut CTRL+N; the idea of private browser screens is that all tracking mechanisms (including cookies) are much more limited. Hence, I think that should be your solution ;-). Alternatively, I sometimes use FireFox, Chrome and Edge alongside each other – one has my admin user, one user with role A, and the other with role B. Finally, I suggest you use the button on the right to quickly change roles

Hope this helps! 

Best regards,

Wouter