In our case our dungeon farming team contains our mains that we plan to play at cap as I plan to raid as a Paladin Healer and I hope my brother will come raid as a DPS Warrior who can off Tank and maybe he will work into Main Tanking at some point (I plan on us getting him BiS gearsets for both roles).

One concern with 4 Shaman+Priest would be heavy water costs unless you have your own mage or a really good friend who is a mage and can be available. My other concern would be lack of a Tank option for any content that needs it.

In BC one of the teams I played was a Druid+3 Shaman+Priest team and between Chain Lighting and Chain Healing it was a nice fun flexible Hybrid group. Sometimes in PVP I would play the Druid as a BoomKin to be kinda like a 4th caster shaman and in dungeons I could make the Druid Tank if I needed to. If I recall correctly that was BC though when the level cap went to 70 and there were significant changes so I can't speak to how viable/fun they would be in clearing dungeons and in World PVP on classic WoW.