NIN has an extremely chunky 16K shield from Huton, and SAM can layer 16K worth of shields from Ogi Namikiri in similar manner if they're hitting multiple targets. The latter in particular can zero out even bigger hits in conjunction with Chiten's 50% damage reduction.

MNK has small, but spammable 6K shields from Thunderclap.

None of those are tanky enough to allowing people to soak things like MCH LBs without taking damage, though...unless they're being layered with shields from other sources like DRK's 8K TBN, WHM's 6/12K from Aquaveil and others.