Yes you can. I had trouble with this as well and got some advice that really helped.
As for the Gmail icon, all you have to do is download the Google Mobile app and if you have a Gmail account, you will have a separate Gmail icon that comes with the Google mobile app.
For any other separate e-mail icons, such as corporate, etc., you can get Empower. It's $20, but for me it was well worth it. Read the thread I originally posted for details: Separate Messages?