Can muslims keep pets such as foxes or wolves because they aren't exactly full breed dogs? Or can they not keep anything that is in the dog family as a pet?
The general view is that everything is permissible unless there is a verse in the Quran or a hadith that would say it is prohibited. Since we know from many hadiths that keeping dogs is not allowed (check the link above in the comment section). However, That was for dogs specifically. The evidence to support my claim is that we don't use foxes or wolves to guard the herd or the sheep.
So you can assume that keeping foxes and wolves...etc is allowed in Islam.