Universality Of Conformal Exchangeability Martingales

Conformal exchangeability martingales provide an example of exchangeability martingales (which are randomized). Are the conformal exchangeability martingales the only exchangeability martingales? Or are there other classes of exchangeability martingales?

A natural starting point is the binary observation space ⚠ $\mathbf{Z}:=\{0,1\}$.