If you are familiar with the Process Framework Admin Tool you could do this with a new task on the design node type:
Always make a backup of your Process schema tables first since you could potentially mess up the workflow for Designer with this tool.
Create a new task on the design node type, call it something like "Open Design (admin)" and make sure only the admin Px Role is selected for this task (so that only Px users with this role can use this task).
Then just put these subtasks in the task:
Change Owner to Self
Basically, create an admin-only open design task that first changes the owner of the design to that user then opens it for editing.
This keeps the Admin from having to separately change owner manually but they would have to change the owner back after they were finished.
You could also create an Admin-only Close Design task (that you would have to run from the ArcFM Tasks drop down tool in ArcMap instead of the Close Design button) that has the Change Owner subtask on it. This way the admin user could close the design with this task and it would pop up the user list to assign the owner back to the original owner (or someone else). Or the admin user could just use the regular close design button to stay as the current owner.
The reason only the owner can edit a design is to keep two users from editing the design at the same time which would cause serious data inconsistency errors.