Grouping words / phrases into categories?

I would like to find a way to have learners group related words together into categories.  (This is a great learning strategy based on theory and research.)  For a very simple example, there is the following list of words:

Persian, Malamute, Poodle, Cat, Dog, Siamese, Tabby, Great Dane, Chihuahua, Manx, Mouse, Snapping.

The learner determines that "cat" and "dog" are the headings of two distinct groups and then clicks and drags each into the heading positions.  Then the learner clicks and drags on each of the remaining terms to place them either into the cat or dog group.  The extra words "mouse" and "snapping" do not apply to cat or dog so they stay where they were.

Does anyone have any suggestions, please?  Is there a custom Engage available from the community that can do this?  Thank you for your help!