Yes, but they definitely shouldn’t. Aura of protection is hardly 5e D&D’s most glamorous ability, but gameplay shows it be one of the most powerful tools in the game (….as if the paladin doesn’t have enough of those already, with the insanely overpowered (IMHO) divine smite and lay on hands).
One aura of protection already provides a massive boost to a party in almost every combat, but once you’ve got two paladins in your party things get insane. Just by staying tight, the whole party could constantly be benefiting from +6 on every saving throw!
And it’s not just an adventuring consideration. What happens if the PCs need to take out a cadre of four evil paladins? Provided the bad guys stayed close to one another, they could easily be getting +12 on their saving throws… I wouldn’t want to be a caster charged with facing them!
Anyway, you probably don’t need any convincing… you’ve already experienced it for yourself, and that’s why you’re here. Well here’s a little house rule you can use to lessen the effect.
- Multiple auras of protections don’t stack if the paladins worship different gods. The creature in question can benefit from just the strongest aura.
- Where two or more auras of protection of paladins who worship the same god overlap, a creature benefits from the strongest aura, with an additional +1 bonus for every extra aura they are overlapped by.