Not sure if this would be feasible... but...
The 'linework' part of the detail would be easy enough. "layer-name-title-1" and "layer-name-title-2". Yes, when you insert your detail frame it will be a bit of a hot mess. And, when you insert the detail into your sheet, it will turn on ALL the detail layers. You would end up need a little script to toggle the right layers on and off, and remember to do it each time.
The text is the tough part. It is probably relocated for each frame. Maybe a different style even? Different size? Would it be possible to change the detail text to annotative? With annotative text you can relocate it depending on the annotative scale. You could create to annotative scales, and name them by the 'design group'. Technically, they are the same scale, but have different names. When you have ANNOTATIVE-STYLE-1 active, the text is in a certain location/size. When you have ANNOTATIVE-STYLE-2 on, it would shift to the second location. Keep the annotative scale and layer toggles in sync.
Its a bit of a coordination issue, but could keep you from having to manage duplicate sets of details.
You could even get fancy... I assume there is a different titleblock for each design group as well? You could create a script... lets call it 'rectify detail frames'. Upon execution, it checks the titleblock that is in the sheet, then toggles the annotative scale and layers accordingly.
This all assumes that you can actually use annotative text as the text that is in the detail right now... if not... well... 2 sets of details it is... or tell your design groups to deal with the same detail frame.
t.