multiple menu locations, multiple weights

For any given node, I'd like the ability to assign it an arbitrary number of parents in the menu system, so the same node can show up in multiple places within the site hierarchy. Further, for each parent I should be able to assign a different weight. I should also be able to designate one of these parents as the "real location" for the node within the site hierarchy. That is where the user will be taken when they click on any of the node's menu links.

For instance, consider a site I will be redesigning in Drupal for a science museum. The site will have a page describing group admission policies that must appear in at least four different locations within the primary menu navigation:

/planning_your_visit/groups
/exhibits_and_shows/imax/groups
/exhibits_and_shows/special_exhibits/groups
/programs_and_events/groups

In some of these menus the node will need to appear near the top of the list, and at some it will be near the bottom. Hence the need for multiple weights. If a user clicks on any of these menu links, the URL and menu would reflect the first path indicated in this list. That is the "real location" of the node. Alternatively, Drupal could remember where the user came from and maintain that location in the hierarchy, but I assume this is a much more difficult task and is not as critical of a feature.