As much as I love the class system in V, I definitely wouldnt do this. I think the 1 character 1 class system is part of what gave FF6 it's charm. If each character could change class there would hardly be a need for there to be 14 characters in the game which would make FF6 majorly lose it's apeal.
Well, one reason for the large number of characters is because a lot of them have major plot relevance. I guess characters like Gau and Mog would lose a lot of their point though.

Anyway that's why I also suggested another possibility would be having a hybrid of the job system and FFVI's system, where characters can learn a lot of abilities but each character has one unique ability.