I believe you're looking for the GRANT ANY OBJECT PRIVILEGE privilege.
The ANY privileges are all very powerful privileges and they often create opportunities for crafty humans to do things that you might not have anticipated. They are generally frowned upon heavily in any sort of audit situation. I'd be very, very cautious about giving non-DBAs these privileges.
It would make much more sense to me, particularly when you appear to want to restrict things to a single schema, to have a DBA user create a stored procedure that does the actual grant (implementing whatever validations, logging, etc. are appropriate) and grant the user the privilege to execute this stored procedure.