Disable Mail notifications for just one account?

I'm wondering if anyone has a workaround to this, as I've been searching around and so far haven't discovered anything.

I have three accounts with mail.app on my 2012 iMac. Two of the accounts are personal accounts and the third account is used for nothing but health monitoring of a very busy network firewall appliance.

Is there any way to completely disable notifications on that account without impacting the notifications on the other accounts?

Thanks.