I have been searching for this solution off and on for about a month and finally found it. Found it through ‘J’s post, Multiple Instances of Mozilla Thunderbird? at http://www.wynia.org, off of a comment by ‘Bortel’. Bortel linked to ‘Run multiple copies of Thunderbird at the same time‘ on the MozillaZine Knowledge Base.

Basically, all you have to do is set the environment variable MOZ_NO_REMOTE to 1 (obviously this is a windows thing and you mac people can figure it out for yourself). If you don’t know how to set an environment variable then learn how to.

If you don’t use the thunderbird email client you can download it for free:

Download Thunderbird