- use any weapon or combat technique,
- simultaneously fight a number of 1 HD or less creatures equal to level.
The real question is: what other "universal" ability, if anything, could be substituted for the "use any weapon" ability? For those who weren't around when I was first toying with two-ability class templates, a "universal" ability is one that uses some kind of universal quantifier/qualifier, like "Any", "All", "Every", "None", "Never", or "Always". It's a sort of trump ability, although it won't always apply in practice: the Thief class as I described it previously can reroll surprise if the character does something distracting, but what counts as a distraction depends on the situation. Similarly, a Fighter can use Any weapon or combat technique without special training, but that doesn't necessarily apply to any non-weapon, just because it could be used as a weapon; I would exclude siege engines and other devices (which would be reserved for the Tinkerer) and any weapon that requires more than one person, unless used in consort with other Fighters or those trained with that weapon.
I'm trying to think of alternate "universal" abilities appropriate to a Fighter, and I can't think of any that would work. "Reroll any damage taken" for some kind of evasive fighter is a bit meta-game-y, as does "Reroll any attack roll". The "reroll any damage taken" rule could work with a qualifier, such as sacrificing a piece of equipment, but that assumes you aren't otherwise using "Shields Shall Be Splintered!" and similar rules.
There might be some potential in thinking about physically direct characters who aren't Fighters. "Adapt to any hazardous environment" is tempting, but has no mechanical context; it would work better as a "scaled" ability, replacing the multiple opponent rule: "get a level-based bonus to the number of turns the character can survive a hazardous environment", with the understanding that "turns" changes to whatever the base time unit is.
Which just goes to show: even without a variant "universal" ability, you can have quite a few Fighter variants without ever creating an actual new class.