There is a little known web browser for the Mac that also has built-in functionality that uses parallel sessions, thus allowing a user to log in to multiple accounts on the same web site:

http://www.stainlessapp.com

I have a couple of Gmail accounts, and when I loaded up Stainless, I logged in to my first account, then hit command + shift + t

A Single Session tab opened up. I loaded up Gmail again, and logged in to my second account.

Both tabs were able to log me in to two accounts simultaneously.

Stainless also runs each tab or browser window through its on process, so if one tab or window crashes, the others stay open.