Tanks
Prot Pally
Blood DK
Unholy DK
Healers
Resto Shaman
Resto Druid
DPS
Boomkin
Ret Pally
Fire Mage
17 Shadow Priests
VE healing assuming 4k dps by shadow priests (HPS below not including JoL, Blood, Dev plague)
Group 1 = Pally Tank + 4 SP (800 HPS to tank and 1600 HPS to SPs)
Group 2 = Unholy DK, + 4 SP (800 HPS to tank and 1600 HPS to SPs)
Group 3 = Resto Shaman, Resto Druid, + 3 SP (600 HPS to Others and 1400 HPS to SPs)
Group 4 = Boomkin, Ret Pally, + 3 SP (600 HPS to Others and 1400 HPS to SPs)
Group 5 = Fire Mage, Blood DK, + 3 SP (600 HPS to Others and 1400 HPS to SPs)
You'd have every caster buff/debuff for damage and could easily run with only 2 healers thanks to 17 VEs, Imp Blood Presence, and JoL. I've seen WWS of groups doing speed runs with 2 healers as it is. This set up is like having lifebloom rolling on 17 raid members and renew rolling on the other 8. Patchwerk and four horsemen are the only encounters I can think of where dual spec would have to be used to add a couple of healers. Saph would be easy mode, not that hes tough now.
I know shadow priest DPS is 8th overall and gaining a couple of dps slots doesn't really make up for their weak output but I just thought it was a cool idea. Rolling on caster drops would really really suck obviously :P