Before revision: We propose an iterated Azema-Yor type embedding in the spirit of Azema and Yor, 1979 and Brown et al., 2001 for any given finite number n of probability measures  which are in convex order and satisfy an additional technical assumption.
After revision: We propose an iterated Azema-Yor type embedding in the spirit of Azema and Yor, 1979 and  for any given finite number n of probability measures which are in convex order and satisfy an additional technical assumption.