Handbook of Liturgical Practice of the Russian Church Abroad
When a Priest and Deacon celebrate alone, the Priest first places the Holy Body in the Deacon’s hand, then in his own, and they say the prayer before communing (it is said either by the Deacon or Priest, according to local custom).
When multiple Priests concelebrate without a Deacon, the chief celebrant places the Body in his hands first, then exchanges the peace with each subsequent priest as they do the same for themselves; and when they all have the Body in their hands, the chief celebrant says the prayer and they all consume.
When multiple Priests concelebrate with a Deacon, the chief celebrant prepares (divides) the Lamb; then the second and subsequent Priests place their portion of the Holy Body in their hands and exchange the peace with the chief celebrant, after which he places the Body into the Deacon’s hand, and finally his own; and then the prayer is said (either by the chief celebrant or the Deacon, as per local custom), and then all consume.
From the chalice, the Priests always consume prior to the Deacons, in order of rank.
(Note: this Handbook contains a separate entry for the order of communing non-celebrating clergy amongst those who have celebrated.)