Manual or algorithmic identification of family members is one option, but I think there's something more to be gained here by understanding the behavior just a bit more abstractly... Shopping moods? Modes? Targets? Tasks? Something, possibly – but I'm only guessing here. The real power could come from actually working with/doing user research and prototyping.
I'd love the chance to work on such a project, actually – I had a chance to work with data from a study on the online shopping habits of mothers a few years ago and there's lots of interesting angles to possibly explore, IMHO.