Like Avatar's Favor 

?  (from XI...) 
I could get behind this, though it opens up a lot of problems.  Such as being asked to use a certain pet that might not be as optimal as another... or being asked to switch a pet mid fight for certain buffs, further sh*tting on our MP conservation.  But if they did give buffs...?
Ifrit: STR Bonus or Melee DPS Increase?
Garuda: INT Bonus or Magic DPS increase?
Titan: VIT Bonus or Defense increase?
(Ramuh): DEX bonus or Ranged DPS increase?
(Leviathan): MND Bonus or Healing Potency Increase?