As far as I know if by another browser you mean one session in IE and one in Chrome or Firefox that "should" work with 2 different user accounts, it will never work with 2 browser tabs/windows from the same browser.

But forcing a single session per user is a "your mileage may vary" kind of thing, if it works for you great, if not it isn't really something we provide support for.

Someone else who needed this implemented it and as far as I know it works but maybe not on 1 machine, 2 users on 2 machines should work fine.

If you or someone else needs this and is not satisfied with how it works you can consider implementing the needed changes to make it work better and submit those changes to me for consideration to include them. If the changes require more than about 10 lines of code then I would also need a contributor agreement on file.