Something like this happened at the university in the city I live in. There was an apparently awful service for signing up for classes called BearTracks [1] and someone made a scraped version of it that was better called BearScat [2]. Eventually the university basically incorporated the better version into theirs (to, I understand, mixed results).

[1] https://www.beartracks.ualberta.ca/ [2] http://www.bearscat.ca/