Outlook 2010/multiple exchange accounts/new mail notification on one only

Hi, is there a way to have multiple exchange accounts in Outlook 2010 but just have new mail notifications on the first only?

I tried having the first exchange account open an additional user, but running into memory errors as a result. Found the solution to that by adding them as separate accounts, but this creates noise with mail notifications, reminders, etc-

Thanks in advance - Joe