Organization hierarchies for employment

Hi! My foundation is in the middle of a conversion to RENXT. Our current practice for corporate hierarchies and employment records has been dictated by out legacy system's reporting limitations; we currently employ every employee to the parent record and list subsidiaries as alternate names and addresses. The only organization that utilizes the database's hierarchy system is the University itself. We are hoping to break out our Alumni employments for better accuracy. For instance, any federal employee is employed to "US Government," with no real way to tell whether they work for the FBI or DoD, etc. We may not be able to build out relationships for every company, but we at least want to do this when there are large numbers of Alumni employees. 


My question is are vertical relationships the best way to do this? Government and healthcare systems are our biggest organization records right now. Would we be able to pull lists of all employees of a company and it's subsidiaries relatively easily by doing this? Is there a good way to link two subsidiaries together directly? Or is this not a good idea? How is this issue handled elsewhere?