I'm just tossing out ideas really... Paladin certainly gets better with Leadership.
[Agree with above poster about the Nightmare of 55 feats]
Anyway, Fibonacci Fighter can be pretty good still. But at killing stuff only, it seems. Somehow, Wizards of the Coast didn't print any bonus fighter feats that grant spellcasting, but they did print Heroics, the spell that grants a bonus fighter feat. Hm.
With all these 55 bonus feats, you'll finally take all the Combat Focus and Mage Slayer feats. Ubercharger + Spiked Chain lockdown helps too. With the Thicket of Blades stance and whatever Stunning Fist feats you can find, you should be good at breaking people down.
A fighter with items that boosted certain stats, could do quite well.
Need Dex, and Int, and Wis for Dodge/Combat Reflexes tree, Combat Expertise/Whirlwind attack tree, and Combat Focus/Stunning Fist tree.
I especially like the idea of Stunning through the Spiked Chain. Use Rapid Stunning and a few of your feats on Extra Stunning to make this work. During a whirlwind attack. If you fail to stun any of the opponents the first time through, Improved Whirlwind Attack lets you hit up to 3 (or more if the iterative attack limit is lifted) of the ones you've missed for another try.
Tack on Pharaoh's Fist and you're virtually guaranteed to lockdown a crowd. (You'll do better in a crowd than a single opponent, since the Pharaoh's Fist is Stunning Burst 1, forcing crowds to make multiple saves vs stunning.) If you can throw in a Bag of Rats, you'll surely stun everyone. Pain Touch will ensure that anybody who's stunned is also nauseated the next turn. Note that anyone who is stunned drops whatever they're holding and can't move, so that's plenty of time to smack the enemy down.
Tack on Defensive Sweep, Defensive Rebuke, Spiked Chain, and whatever other lockdown features you have, and nobody will every be able to escape.
Use your normal feats to get extra reach (via that Aberration stuff in Lords of Madness) for extra happiness. It makes your Whirlwind Attacks much better too. Permanency on your favorite enlarge person spell too?
Obviously, the Cleave chain, and Power Attack will help with the damage output for whenever you don't need to/can't stun someone.
And it might be cheap, but if you use Leadership to get an Inspire Courage optimized bard, you'll do far better than anyone other class in beating everyone up. [Power Attack 55, anyone?]
At any rate, I'm pretty sure this Fighter has to be Tier 3; it's definitely better than warblade, crusader, and swordsage. Can they ensure that they kill everyone they decide to attack? I don't really think so. At Power Attack 35 (bonus dmg 70 for every attack), the Fighter is essentially at the same BAB as warblade/crusader. Iron Heart's [Warblade's] 9th lvl Strike is +100 dmg, but only on a single attack. Diamond Mind's [Crusader's] is somewhat better, as it grants two full attacks, but that doesn't really compare against the total lockdown that this fighter has.
Utility-wise, all I see is the Shadow Blink for Swordsages (the swift action 50' teleportation), and the dual Stances for Warblades, but nothing else really stands out as awesome. Can someone tell me what's so good about the initiates? If they're Tier 3, I'd say that the Fibonacci Fighter is also Tier 3. I don't really see any spellcasting/game-breaking abilities in any of these classes.