Yes, I think "An and me" should be allowed. Although "non-standard" English, it is surprisingly common. It's far more likely a native speaker would say/write "An and me" rather than "An and I". This is the difference between descriptive grammar (how it's actually used) versus prescriptive grammar (how it should be).
An and I are the subject of the sentence, that means they perform an action (verb). E.g. An eats, "An" is the subject. I eat, "I" is the subject because it performs an action. But in, An sees me, "me" is the object, because the action is performed onto the object by the subject, in this case, by "An".