Hierarchy between terms from different vocabularies in Drupal 7? Is there a way to have a hierarchy of terms by reusing the same terms that reside in different vocabularies? There seem to be so many different options for dealing with taxonomies in Drupal 7 that it feels very daunting to figure out...  

For example, let's say I want to make a directory of athletes for different sports. I've created 3 vocabularies, each with several terms:  

Vocabulary: Sports
* Soccer
* Basketball
* Baseball  

Vocabulary: Divisions
* Division 1
* Division 2  

Vocabulary: Teams
* Team 1
* Team 2  

Each type of sport will be divided into Divisions and then into different teams per Division.  

The hierarchy looks like:  

Soccer
* Division 1
    --Team 1
    --Team 2
*Division 2
    --Team 1
    --Team 2  

Basketball
*Division 1
    --Team 1
    --Team 2
*Division 2
    --Team 1
... and so on for each sport.

Since the terms for vocabularies Divisions and Teams are always the same, I'm thinking it would make more sense to be able to reuse the same terms under those two vocabularies instead of creating the same terms over and over again for each sport, each division...etc.?

Is that even possible and if so, what would be the best way to go about implementing it?
You can make a term reference field on a vocabulary. 
So on a the team vocab one of the fields would be "division".
So when you create a new team you would enter the team name and "tag" the division it is in using auto complete or a dropdown.