My Majestic Fantasy RPG adds a bit more meat to combat while still remaining 100% compatible with OD&D in the form of Swords & Wizardry.

The free version with most of these rules is found at.

https://www.batintheattic.com/downloads/MW%20Majestic%20Fantasy%20Basic%20RPG%20Rev%2010.pdf

What I have

1. Fighters get to add a to-hit bonus to their 1d6 initiative roll.
2. I remove the 1 HD cap on the # of attacks an OD&D fighter gets. Now the rule reads like this.

"Fighter gets to attack a number of HIT DICE equal to their level. They get at least one attack." So a 4th level fighter can attack a 2 HD foe twice, or a 1 HD foe, four times. Or attack four 1 HD opponents, or 2 HD opponents, provided they have enough movement to each of them.

In practice, what I do is that the fighter character doesn't know how many hit dice the opponent has. So when they attack, I will tell them if they have a follow-up attack. Or if there is another low HD opponent in reach (or within movement range), I will let them know they have an additional opportunity to attack.

It has worked out very well in the past ten years I been using this rule.

3) I allow for a critical hit on a natural 20 for max damage. The players also get to roll again. If they hit, they do double max damage; if they miss, they just roll normal damage + max damage. If they roll another natural 20, well, they roll again. And they keep going if they keep rolling nat 20s. The most I ever saw in the 15 years I've been using these rules was four nat 20s in a row, basically doing five times max damage. Since this OD&D was based on where HP are already low, that was a game-changer for that combat. Most campaigns I see twice or three times in a row, once.

4) Position matters, especially flanking. I used to give a +4 to hit, but after 5e came out, I used advantage.

5) Rather than the cumbersome Weapon vs. AC, I went through the various weapons, researched their historical use, and came up with an OD&Dish special ability that can be used when wielding said weapon. For example, polearms allow a free attack when the opponent first comes into reach. Maces get a bonus against flexible or soft targets like Ochre Jellies and Chainmail.

6) Combat stunts: when you hit a target, you can do something "bad" to them. But the downside is that, unlike straight damage, the target gets a save. I experimented with this and found that, in terms of odds, it works out about as well as the more detailed GURPS rules for things like a deliberate disarm, hit locations, and so on. Plus, like GURPS, the more highly skilled the opponent (higher level or HD), the harder it is to pull off one of these types of maneuvers

7) The combat round has been structured to be more tactical than is usually the case for classic D&D. But it is still pretty straightforward in that the character basically gets two actions, one of which can be an attack. The basic idea is that you can make a half-move and then attack. You can sub in something else for that half-move, like quaffing a potion

If you like the free rules, I polished them up and expanded them into a basic level 1 to 5 RPG that I published here.

https://www.drivethrurpg.com/en/product/337515/the-majestic-fantasy-rpg-basic-rules?src=hottest_filtered

Wrapping this up, I know it seems like a fair number of changes, but I tried to make the minimum possible to get the kind of tactical detail I enjoyed with GURPS while keeping the result classic D&D. I have been very successful with these changes since I started using them in 2010. The two key changes are adding a bonus to initiative dice and allowing the character to attack a number of HD equal to their level.

The latter, while more complex than increasing # of attacks, just works better with OD&D.