Deleting old accounts from Mail
I would remove the old accounts for the sake of organization, especially if their details, or even addresses are the same (it sounds like they might be, just with different mail server configurations). You can archive old emails on your mac using the mail app. With the mail app open, go to the menu, click Mailbox -> New Mailbox. This will allow you to create a local mailbox:



Click OK, and the mailbox will be created. Copy all emails you want into this mailbox. It may help to create multiple local mailbox for organization purposes. Once all of your old emails are moved to local storage, you can remove the old accounts while keeping all of your old emails safely on your Mac.