It would be nice, but considering the fistfights which have broken out between Catholic priests and Orthodox priests at the Church of the Holy Sepulchre over minor issues such as whether a door should be closed during a procession, it does not look to me like it is coming anytime soon. Or take a look at the big deal that the Orthodox make out of Purgatory. According to their catechisms and the declarations at their Councils, the Orthodox teaching is virtually indistinguishable from the official Catholic teaching on Purgatory and yet they make a mountain out of not even a molehill.
There was an article a while back in the Catholic newspaper Our Sunday Visitor about an incident which arose when a few Orthodox monks cleaned up a sidewalk area at the Church of the Holy Sepulchre. They had done this voluntarily and in good faith. But after it was all done, the Catholics said that the Orthodox had to undo all their work and place it back into its unkempt state as it was before, since the Orthodox did not get the permission of the Catholics before they had done the work. Where is the Christian charity and understanding at the Church of the Holy Sepulchre where Our Divine Lord was crucified and buried?