Multiple instances of fieldgroup within a node

I've seen this issue brought up elsewhere, but the forums stray off topic and some of them are impossible to navigate: http://drupal.org/node/119102.

Can I create a set of fields and then group them together using fieldgroup - and then create multiple instances of that group within a given node?

A simple example (not my use case): You have a resume node. You have a set of fields grouped together under a group called "Reference". These fields are first name, last name, phone number, job title, etc. Now, clearly you would want to allow the user to add more than one reference! But I would need a way to make multiple instances of the group of fields that make up a reference, within a given node.