Looking for a variety of abilities to cover different archetypes is good. That's the problem with the fighter in the first place is that his only real flavor is "mundane fighter guy", which doesn't leave much room for super powers when it comes to willing suspension of disbelief.
Then you're simply not reading enough fiction.
Using your previous barbarian example, you say he should suddenly become a shaman and start pulling spirits out of a hat and floating whitout strings. Except that's not what people expect of a barbarian at all. That's what people expect of a shaman.
Now take, for example, the hulk. The hulk fights gods now and then in the marvel universe, has conquered whole planets when on vacation, and beated the crap out of the supreme sorcerer on his personal realm. And he can't fly or pull spirits out thin air or has a totem of some fuzzy animal. What he can do is:
-Jump extremely high (he once reached the moon that way) or throw giant boulders that knock his oponents out of the skies.
-Break pretty much anything with his bare fists, including but not limited to magic barriers.
-Clap his hands to create waves of air.
-Shrugg off pretty much anything.
-Clap his hands to create waves of air.
-Slam the ground to provoke earthquakes.
And that applies to plenty of other comic "mundane brutes".
Then there's guys like batman and captain america that have super kung-fu that allow them to dodge/block pretty much anything. A warrior NPC can't block a fireball. Captain America can block freaking super-novas (it hapened in the comics) with his shield! He can then throw his shield to ricochet at impossible angles to knock out an enemy spellcaster for long enough to close in, and then grapples them regardless of they having freedom of movement or not. Then makes a super-patriotic speech that allows his allies to break out from that fear effect that was locking them down. While batman can probably make fear effects of his own.
Really, some people say that batman and superman don't adventure togheter, but if you look at the comics, you can see stuff like:
-Need to go to Apocolopsys that's in another planet. Batman tracks down a teleporter machine and the coordinates with his detective-fu.
-Arrive to Apocolopsys. Superman uses his invulnerability and super-strenght. Batman uses his super kung-fu and super-yoga to slip unnoticed trough darkseeid's magitech sensors, knocking out darkseid's minions from the shadows. And then when superman gets knocked down by darkseid himself, Batman jumps out from the shadows and manages to hurt Darkseid with super kung-fu, and then revitalizes superman with cynical speech!
Simply put, the mundane warrior still fights in a mundane way, it's just that he can go over mortal limits. He hits hard enough to break walls of force. He blocks well enough to stop area effects. He jumps good enough to reach oponents in the air (or throws something to force them into the ground, even if there's raging winds between them). He maybe can literally kick people into next week!