Are there any ecumenical movements among lay people working to unite Roman Catholics and Orthodox Christians?

If leaders of Roman Catholic and Orthodox churches are still far from resolving the theological issues separating these two true churches, is there any ecumenical movement at lay people level like the [Taize fraternity](https://en.wikipedia.org/wiki/Taiz%C3%A9_Community) where Protestants and Catholics live and worship together? Are there Christians from both sides who recognize the truthfulness of the other side and are longing to share the richness of these two traditions despite the opinions of their respective church hierarchies?