There's X-Change Students, by H. Torrance Griffin, a crossover with Generation X. To the best of my knowledge the fic is unfinished (and took a ridiculously long time for me to find).
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Shinji: Well suppose some mysterious entities were attacking, and
Asuka:Oh please, Baka Shinji, that sounds like some cheap, pseudo-profound T.V. show. Low budget. Ambiguous ending.
-Asuka and Shinji discussing why you would build a giant robot. NGE: Shinji Ikari Raising Project Vol.6