Yep, it's not only happened before, it's happened with BATMAN before...Knight said:Has there ever been new episodes of two different versions of the same character being aired at the same time?
In 1977, The New Adventures of Batman by Filmation started airing on CBS. Meanwhile on ABC, Hanna-Barbera's The All New Super Friends Hour started airing that same year. And of course, Batman and Robin were both members of the Super Friends.
Different continuities, different shows, different networks, different animation studios, same characters.