What other out of combat utility could martials be given?

I don't think there'll ever be parity as long as some people can see the future and teleport across continents, but that doesn't mean there's no reason to try to reduce the gap. For instance, back when maneuvers were good I remember using one called Ancient Mountain Hammer to smash my way through an iron door, since it ignored hardness (how the game represented object durability at the time).

Which has got me thinking, other than the old method of getting handed a keep and a few hundred minions what forms of utility could reasonably fit in the martial purview? Basically what stuff is superhuman (a high level fighter can already do a number of completely impossible things like wade through lava and heal their blackened flesh by relaxing for an hour) but not supernatural?