It isn't possible.
Probably the closest you could come to it is a multi-select matrix, but that wouldn't include ranks.

Agreed with TomG , you can also break the question, first create multichoice questions for each group and then carryforward the selection to new rank order question for each multi choice questions.

Interesting. I don't actually care about the rank ordering and just need the drag and drop function. Does that change anything?

rondev you mentioned creating multichoice questions for each group...where can one create multichoice questions by group? Thanks!

https://www.qualtrics.com/community/discussion/comment/27338#Comment_27338No, you can use a Matrix drag and drop instead which doesn't have ranks, but that is still only single answer. As I said previously, you could use a multi-select Likert matrix instead. It will give you the data you want, but is a different user experience.