The Byakugan, despite it's name is not actually white. In the anime (as I was just watching), it's actually kind of purple. You know what other doujutsu is purple? ... Rinnegan. Perhaps Juubi eye+Byakugan == rinnegan. It would make sense if a mutated byakugan plus the juubi's yin later developed into the sharingan. Just some thoughts. I hope Kishi will explain the history of the So6P in full at some point...