Limit Taxonomy lists in a node edit page

Here's a bit of a tricky question, hopefully I can communicate it clearly.

I'm facing a problem where I need to limit a specific taxonomy list based on the values selected in two other taxonomy lists (on the node edit page).

Example:
Node A has three vocabularies: Faculty, Level, Subject

Can I filter the list presented under Subject to values that match a pre-selected combination based on Course and Level? As in, if I select a faculty of Math, a level of 101, the resulting drop down for Subject will be filtered to match a list specific to that combination.

Has anyone ever had to tackle a problem like this in Drupal? Any advice would be appreciated!

Thanks!