Then there’s the “one attack per level against creatures with one/less than one hit die”, originating from Heroes in Chainmail having the fighting ability of four men. This rule is sometimes called "cleave". The same ability is also pointed at underneath the “Melee attacks per round” table in AD&D, referring mysteriously to the COMBAT section, which offers no explanation on the matter.
A rather popular rule for “cleaving” weak foes that doesn’t require you to track the number of attacks is what I have just decided to call “If They’re Slain, Swing Again”. It grants a free attack each time you slay an enemy, continuing as long as you either fail to score a kill or there are no more enemies within reach. The less hit dice the opponents have, the more likely you are to get multiple attacks off.
Here is yet another option I came up with which combines aspects of both extra attacks and cleaves:
Ability: Fighter's FocusIf you hit an enemy with an attack on your turn, you can attack one more time. If this second attack is a miss or a non-killing blow, your turn then ends. However, if it is a killing blow, you can attack again, and keep attacking as long as you keep landing killing blows, or until there are no more targets within range.
RationaleThe condition of Fighter's Focus means that you get a sort-of-an-extra-attack, but not always - only when the first blow lands. It’s like gaining momentum in the melee. Then on the second blow, you really get into the zone and potentially start mowing everything down. Perhaps you could give these two "modes" of focus different names to help players remember how they work. (If I have to draw a flowchart, or nobody remembers how it works, then it must be a bad rule.) It also means that you don't need to keep track your alternating rounds like in AD&D.
Obviously, the second stage of focus still works best against low-HD creatures, while the first part gives more of an advantage against mushy enemies with poor AC. Thus it will sometimes give you an edge against high-HD creatures, too. All in all, the ability should end up being less powerful than straight up giving Fighters two attacks, but more powerful than the “If They’re Slain, Swing Again” rule by itself. It’s somewhere in between.
I’ve been exploring these different options recently since I’m looking to change some rules for the next game I run. Specifically, breaking from LotFP, I want to give non-Fighters the increasing to-hit that they get in B/X. But I still want Dwarves and Elves (and Paladins etc. that I may add) to have the improved combat options, as they do in LotFP, and have no equipment restrictions. So with Fighters losing their only niche, what do you give them so they don’t fall behind? Well, more attacks, of course.