Editable Shares with named user Admins from Generic Admin


we have one company, they want, that we use named Admins to create sharefolders for users and customers.

Our Problem is, on the existing Instance many shares are on the generic Admin.

How can i make usable the shares for the other named Admins? I already add all named admin Accounts to the admin group.

Group Folders are not the solution for us, cause the shares already exists and also its a third party coded App and if the app are not compatible for newer versions in the future, we have a big problem.