I have, next to my own domains, also the email accounts for automated services and customers. I do not want to recieve those notifications. They distract me from my normal work. However, I have one automated service which only notifies me when a serious problem has arrised. I always need to be aware of these messages. A different sounding notification would be very helpful there. I can imagine that people might also have a wish for not showing the content of their private mail in the notification, but want to see that content of business mail. Perhaps even have a different colored notification based on the account.
My idea therefor is to move the location of the notification settings to the account (or for maximum configurability, to the folder level) settings. This makes per account (or per folder) configuration of separate notification settings possible. Possibly with the addition of notification-color.