Contributions- on behalf of existing organisations only?
If you are using Drupal you could potentially set this up using webform-civicrm since that allows you to set the Organisation fields to require it to be an existing contact.
For Contribution Pages in general, the 'on behalf of' works on principle that an individual is signing up and registering that the membership belongs to the Organisation. I am not sure that maps so easily to a situation where the administrators are doing all the work, which is what i understood from your description.