Name of a card sorting technique that lets people sort only their favorite items?

I'm working on a software tool that one of my clients uses on their intranet. We are planning to run a card sort study.

Let's say the top 2 levels of their existing IA look like this:

Menu item 1 - Submenu item 1 - Submenu item 2 - Submenu item 3 - Submenu item 4 Menu item 2 - Submenu item 5 - Submenu item 6 - Submenu item 7 Menu item 3 - Submenu item 8 - Submenu item 9 - Submenu item 10 - Submenu item 11 - Submenu item 12 - Submenu item 13 - Submenu item 14

We are trying to determine 1) the best items to put at the top level of that menu and 2) any subcategories that are needed in order to be able to easily add more items in the submenus without making them too complex. This may be done in different studies.

Since their company is global and the users have a very wide variety of specializations, they are often use one area of the application that points to their specialization heavily and then have a few other areas they use a little bit and some that they don't understand at all. We might have:

• User A: Uses items in menu 1 extensively and a few items in menu 3, but knows nothing about any items in menu 2 because that is not his focus.
• User B: Uses items in menu 2 extensively and most items in menu 3, but knows nothing about any items in menu 1 because that is not her focus.

But we can't create a whole bunch of different card sorting studies based on each possible specialization because there would be too many. Our studies would involve both present and future capabilities of the software. We're also trying to determine the best top-level menu structure, and forcing users to put every item somewhere would hurt the quality of our data.

We're talking about doing a type of card sorting study where we get people to identify the items they would most commonly use (or that they know about) and then sort those.

There are a couple ways to achieve this: telling participants to stop once they have sorted all items they know about (which would raise another question of participants wanting to stop before they are done) or telling them to create a bucket for items that they don't know where to put (which makes standardizing the data more difficult).

We would like to find out more about the type of card sort we are trying to do, to see if any vendors provide software that is specifically for this. Is there a name for this kind of card sort?