I finished setting up Galaxy Gameworks with Google mail and apps services today, and was immediately frustrated by the inability to have my business e-mail and my personal e-mail open at the same time.
I did a little digging and found that Google has indeed made it possible to have Gmail and the core web apps open on two different accounts. However, setting it up is a little tricky.
You can turn on this feature by going to Settings -> Accounts -> Google Account settings, and then editing the “Multiple sign-in” setting. Once you have done this and refreshed your browser, you can click the downward arrow next to your account name in the upper right and log in with another gmail account.