Help: 2nd E-Mail Account in mac.mail.com

[Albert D'Amanda]

I am having problems adding a second e-mail account/new address  using 
the same Incoming mail server mail.mac.com

According to mail Help:
Open Mail Preferences ;
*Select add(+) POP ;  type in a new account name  and  a new  e-mail 
address;
  *Keep the same incoming Mail Server (mail.mac.com) and type in a new 
User name and new Password.
Close and Save.

When I send a test message to the new e-mail address from my existing 
e-mail account, I get error messages asking me for my password( for the 
2nd account). When I re-enter it , I get errors messages saying that 
mail.mac.com does not recognize the password for the new account.
Get a returned mail notice-telling me that mail.mac.com does not 
recognize the new alias

Bottom line is that apparently  I do not know what I am doing wrong!

  My question is:
Has anyone out there , using mac.mail.com  , successfully opened up a 
second  e-mail account and how did you do it?

BY THE WAY: I have not even addressed the Outgoing Mail Server (SMTP) 
block, but that comes later!

Thanks to all that reply

Albert
Dual 1.25 GHz PowerPC G4
1.75 GB DDR SDRAM
Panther 10.3.2