Virtual spatial vectors in electrical engineering

I keep wondering whether the 3 vetors(R,Y,B) spaced 120 electrical degrees apart that we write on a sheet of paper- are in a plain?- say x plain. So we call them Rx, Yx, Zx

Can we have similar 3 phase vetors in say Y plain and 3 more in Z plain? Now we will have additionally Ry, Yy, By and Rz, Yz, Bz. Then what will be the electrical/ mathematical relation/ vector transformation relation between these vectors?

If this is practically possible, we can use it in transmitting signals with 3 times capacity per channel. Many more applications can be found. I have written a lengthy paper, but unable to attach it here. I got bogged down in mathematics, and in actual practical construction.
Can I get any help?

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