The notification is sent out to the customer, I as a service provider, would like a copy of the same notification to be sent to my (or any specific) e-mail address.
The easiest way to achieve the desired result is including the required e-mail address to "BCC Address":
Home> Communication Director> Notification Manager> Notification Templates
find a template which is sent out to the customer, click Edit button add an address to Bcc Address field. Other people (the customer) who receive the notification will not see BCC addressees in the recipients list.