Would absolutely love a feature like this - it does not exist in WHD unfortunately.
As long as the ticket has an assigned due date attached, you can accomplish this with action rules and request types. Create a request type that is visible to only upper level techs and managers or admin and assign it to the ticket. Create and actions rule and under the Criteria Tab select Date> Due> Within the Next> "X"> Business Days and Request Type> Is> "X"
This will only work for one request type at a time. If the tickets are needing multiple request types then you would have to create an action rule for each request type to change it too and a hidden request type to make it disappear. This can be accomplished by creating child request types in your system. Since the primary request type needs to be hidden, you can simply create a group and assign a small amount of techs to the group to manage these tickets. I hope this helps.