>>282957576
There were lots of fanfics and doujins which tackled it in their own way. But Anno had no interest in an official continuation. Putting that aside, any continuation story would be very different from the show. It would have to be a survival/slice of life/romance story, with essentially no other elements. Fairly different appeal.

Tl;dr go digging through old Eva fanfic archives or read Re-Take, there's a lot good there.