Handbook of Liturgical Practice of the Russian Church Abroad
When multiple Priests concelebrate, only the senior Priest (i.e. chief celebrant) prays the threefold Cherubic Hymn and the Prayer of the Third Hour with uplifted hands, at their appointed place in the Divine Liturgy. He repeats them thrice, in the normal way, with the Deacon(s) sharing the refrains as prescribed. If there is no Deacon serving, the senior Priest says both the prayers and the refrains.
It should be noted that this not an altogether universal practice, and even within the Church Abroad there have existed certain places in which concelebrating Priests are blessed to distribute these prayers amongst themselves, the senior Priest saying the prayer the first time, the next Priest the second, and so on (similar to the way that concelebrating Hiearchs rightly share these prayers); however, this practice is not blessed to be done in our Diocese.
The reason that these prayers are not ‘shared’ is in order to preserve the liturgical reality that each Divine Liturgy is in fact headed by one chief celebrant, together with other clergy who co–celebrate with him; which reality is itself a confession of our belief that we have One Great High Priest, Who is mystically the celebrant of these Mysteries. Thus while elements of the Liturgy are shared between concelebrating Priests (e.g. exclamations at the litanies), the chief acts of consecration (of which the two prayers presently being discussed are part) are reserved to the chief celebrant alone.