I think it is common to sing the slow Great Doxology in fourth mode "Legetos" by Petros Lambadarios. Similarly, the Cherubic Hymn and Communion Hymn in fourth mode.
The "agrafon typikon" (unwritten typikon) confirms the above (refer to Dimitrios Ioannidis' book and Asterios Devrelis' Theory of Byzantine Music), and that is the general traditional practice.