You can run multiple sessions of most email programs simultaneously. However most mailers allow you to manage more than one address from a single session even where they are from different mail servers.
Mailers vary in the facilities they provide to automatically sort and respond to messages from different servers. Microsoft Outlook does it but is kind of clumsy.
Easily the best at this aspect is Pegasus. It can do pretty much anything imaginable. Its filtering capabilities are awesome and it can automatically switch between identites and mail servers based on the folder being worked with. It is free, well documented and has an excellent online support group.
www.pmail.com