I think you may be confusing email applications and email providers.
Email Applications on a Mac
-Apple Mail
-Mozilla Thunderbird
-Microsoft Entourage/Outlook
Email Providers
-Apple iCloud
-Google Gmail
-Microsoft Outlook/Hotmail/Live/MSN
-Yahoo!
-Comcast/TimeWarner/Charter/etc. - cable ISP (Internet Service Providers)
If you already have a Gmail account, and it is already added to the Mail app, you would have to first create a new account with one of the email providers in the list. You can then add it to the Mail app, or use another email application and add it there if you want them totally separated.. You cannot create a new email account directly in the Internet Accounts or Apple Mail app.
I use the following:
-Apple Mail - 3 different email accounts on my iMac, 3 different email accounts on my Mac mini
-Microsoft Outlook - 3 different email accounts on my work MBP and MBA
-Mozilla Thunderbird - 6 different email accounts on my iMac
I could actually add them all to the Apple Mail app, and they would all show as separate accounts in the sidebar.
That make sense?
C