"Public - No Access" Data Sharing Setting

"Public - No Access" Data Sharing Setting

Would it be possible to add a Data Share Setting level between private (where the record does not even appear in the module view) and public read only (where everyone has the ability to access and read every detail from the record)? I want everyone to see that the record exists in the module view with perhaps a few details, but I do not want the entire record to be accessible/readable. Essentially, it would be a locking function, but one that prevents access rather than just write/delete capabilities. Those without permission would not be able to open or access the record, but they would still be able to see that it is there in the module view.