Trying to think of which alliance raid fights actually need multiple tanks (leaving out if, y'know, the MT dies, because that's largely unpredictable). Correct me if I'm missing something...
Labyrinth of the Ancients:
-Bone Dragon is designed for multiple tanks, one to tank the Dragon, and others to pull the skeletons away, so that the party will have more time to burn them down when they start to leash back to the Dragon. However, gear creep has made this largely irrelevant.
-The Atomos room splits the three parties, and each party is intended to need their own tank to handle the adds. But, again, gear creep means they melt anyway.
-Thanatos, due to only being vulnerable to one party at a time, requires the next party's tank to take over if the previous party's buff runs out.
-The three gargoyles before King Behemoth need to be kept apart.
-The iron giant adds on King Behemoth and Phlegethon are supposed to require a tank, but again, gear creep.
Syrcus Tower:
-The adds on Amon may need to be tanked, but once more, gear creep means they usually die fast enough to not matter.
World of Darkness:
-The Atomos split the party again. Tanks mainly need to watch out for the adds.
-Cerberus needs one tank on the boss and one tank on the adds during the belly phase. May need the third tank in the belly as well, depending on how quickly the swallowed party can take them out.
Void Ark:
-When the final boss splits into three, they need to be split up.
Weeping City of Mhach:
-Ozma requires all three tanks for soaking tankbusters and holding adds, and for the Ozmashade phase when the parties are separated.
Dun Scaith:
-Scathach requires a second tank to pick up the Conla add, otherwise it tethers to the boss and explodes, usually causing a wipe.
-Diabolos only requires a second tank if the group going into the Deathgates fails and the add spawns on the raid. This really should not happen, but I've seen it.
Rabanastre:
-The add phase on Hashmal requires all three tanks to pick up their own sand golems, although these days he usually goes down before he gets to that mechanic.
-Rofocale requires all three tanks during his add phase while each party has to take their own add down.
Ridorana Lighthouse:
-I can't remember any need for multiple tanks here. Feel free to correct me.
Orbonne Monastery:
-Like Ozma, The Thunder God requires all three tanks for soaking hits, and for keeping the adds separated.
Copied Factory:
-The second boss, again, requires three tanks for soaking hits.
-Engels and the Walking Fortress both have more add phases that need to be split up.
Puppets' Bunker:
-The first boss, once again, requires three tanks for soaking and add management.
-The trash right after the first boss, while not technically requiring multiple tanks, is a lot easier if each tank focuses on one of the big mobs to interrupt their AoE paralysis attack.
-The second boss is three bosses, each needing their own tank.