Thunderbird can have many mail accounts. If you have two or more email addresses, you can create a mail account for each and receive mail from each server into thunderbird. You can, but do not have to, forward all mail from various email addresses into one server and then download to TB. You could forward emails from one email address to another using a Message Filter in Thunderbird, but this is best done via logging on to the webmail account using a browser and setting up forwarding to the a different email address. There is little point downloading all the mail from one account just to resend/forward to another server and download it all again.