Oppositional schools work really well if there are an odd number of schools because every school can have two oppositional schools.
Being visual, though, here is a star to show every school and its two oppositional schools. Pick a school, say Conjuration/Summoning. Following the lines away from Conjuration/Summoning, you find that the two oppositional schools are Invocation/Evocation and Greater Divination.
Many of the schools have the same oppositional schools as printed in the PHB. I added a school, so not all of them are the same, but enough do that it feels right.
Yes this makes it harder to add more schools, but I'll upload that diagram soon.
Let me know what you think.