I have 3 email accounts.

One of them is not really important for me, but unfortunately I need it, because this is my business email address, and sometimes my boss asks me search for something in the account.

However, I don't need notifications for from new emails from this account.

I have set the desktop notification, and sounds, now the only thing I still want to change is the new mail envelope on the icon:

What can I do so this icons doesn't appear for email to business account? (the other accounts need it!)